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Lately, there has been a renewed interest in fermionic 1-body reduced density matrices and their restrictions beyond the Pauli principle. These restrictions are usually quantified using the polytope of allowed, ordered eigenvalues of such matrices. Here, we prove this polytope's volume rapidly approaches the volume predicted by the Pauli principle as the dimension of the 1-body space grows, and that additional corrections, caused by generalized Pauli constraints, are of much lower order unless the number of fermions is small. Indeed, we argue the generalized constraints are most restrictive in (effective) few-fermion settings with low Hilbert space dimension., Comment: Published version; 37 pages, 5 figures

We prove that on any two-dimensional lattice of qudits of a prime dimension, every translation invariant Pauli stabilizer group with local generators and with code distance being the linear system size, is decomposed by a local Clifford circuit of constant depth into a finite number of copies of the toric code (abelian discrete gauge theory) stabilizer group. This means that under local Clifford circuits the number of toric code copies is the complete invariant of topological Pauli stabilizer codes. Previously, the same conclusion was obtained under the assumption of nonchirality for qubit codes or the Calderbank-Shor-Steane structure for prime qudit codes; we do not assume any of these., 19 pages, (v2) removed the need of Clifford QCA of v1 using recent results (v3) some clarification, minor rewording

We calculate exact solutions of the Schrodinger equation for a particle constrained to move along a spherical surface and interacting with non-central potentials, namely, (i) Makarov, (ii) ring-shaped pseudo-harmonic oscillatory, and (iii) Kratzer potentials. We also study exact solutions of the Pauli equation in the same geometrical setting for a charged particle in the presence of a uniform magnetic field. In this case, the two-component spinor can adhere to the surface only if the magnetic field intensity has certain special values. The solutions of Schrodinger equations allow us to obtain exact Pauli spinors and their corresponding energy eigenvalues for the same non-central potentials.

We study the density of states of the Pauli Hamiltonian with a Poisson random distribution of smooth finite-width vortices and we obtain classical bounds for the Lifshits tails for them. These Hamiltonians are smooth approximations to the self-adjoint extensions of the Aharonov–Bohm Hamiltonian. In this case because pairs of impurities are coupled by the magnetic field we cannot use the Laplace characteristic functional.

The properties of A-statistics, related to the class of simple Lie algebras sl(n+1) (Palev, T.D.: Preprint JINR E17-10550 (1977); hep-th/9705032), are further investigated. The description of each sl(n+1) is carried out via generators and their relations, first introduced by Jacobson. The related Fock spaces W_p (p=1,2,...) are finite-dimensional irreducible sl(n+1)-modules. The Pauli principle of the underlying statistics is formulated. In addition the paper contains the following new results: (a) The A-statistics are interpreted as exclusion statistics; (b) Within each W_p operators B(p)_1^\pm, ..., B(p)_n^\pm, proportional to the Jacobson generators, are introduced. It is proved that in an appropriate topology the limit of B(p)_i^\pm for p going to infinity is equal to B_i^\pm, where B_i^\pm are Bose creation and annihilation operators; (c) It is shown that the local statistics of the degenerated hard-core Bose models and of the related Heisenberg spin models is p=1 A-statistics., Comment: LaTeX-file, 33 pages

The algebra of conserved observables of the SO(4,1) gauge-invariant theory of the Dirac fermions in the external field of the Kaluza-Klein monopole is investigated. It is shown that the Dirac conserved operators have physical parts associated with Pauli operators that are also conserved in the sense of the Klein-Gordon theory. In this way one gets simpler methods of analyzing the properties of the conserved Dirac operators and their main algebraic structures including the representations of dynamical algebras governing the Dirac quantum modes., Comment: 16 pages, latex, no figures

We consider purely magnetic two-dimensional Pauli operators H with a spectral gap, perturbed by a magnetic field λBs=λdas, λ⩾0. Assuming that Bs and as vanish at infinity, we ask whether eigenvalues will cross the gap as λ→∞. Furthermore, we give an example of a two-dimensional Pauli operator H with periodic magnetic field of zero flux which has at least one spectral gap.

Canonical and quasi-canonical realizations of the osp(D|d) superalgebra are presented. In these realizations there is only one independent Casimir operator: The quadratic one C, the eigenvalues of which allow specification of the involved representations. Pauli’s method for solving the spectrum of the Coulomb problem through quantization of the Runge–Lenz vector is extended to an arbitrary dimension superspace E(D|d) with D bosonic coordinates and d (even) fermionic coordinates. The symmetry algebra of the Hamiltonian is the superalgebra osp(D+1|d). It is shown how the energy spectrum is related to the Casimir operator C′ of osp(D+1|d) in its quasicanonical realization. Then the energy levels are given in terms of the eigenvalues of the operator C′.

Forms of canonical (Bloch) and Dirac density matrices for free electrons with and without external applied fields are first considered. The basic tool employed is the Bloch equation with a one-electron Hamiltonian. Such an approach is used to obtain a perturbation theory to all orders for the idempotent Dirac density matrix when a common potential energy V(r) is switched on to originally free electrons. The relation to density functional theory is then considered and the exchange–correlation contribution Vxc(r) to V(r) is expressed in terms of first- and second-order density matrices following Holas and March. These latter density matrices are now for the fully interacting system and, in particular, the first-order density matrix is no longer idempotent, though it must still satisfy generalized Pauli Principle conditions. Reference is also made to a localized Wigner electron in a strong magnetic field.

Diamagnetism of the magnetic Schrodinger operator and paramagnetism of the Pauli operator are rigorously proven for nonhomogeneous magnetic fields in the large field, in the large temperature and in the semiclassical asymptotic regimes. New counterexamples are presented which show that neither dia- nor paramagnetism is true in a robust sense (without asymptotics). In particular, we demonstrate that the recent diamagnetic comparison result by Loss and Thaller [M. Loss and B. Thaller, Commun. Math. Phys. (submitted)] is essentially the best one can hope for.

In the Fock–Bargmann space, the complete harmonic‐oscillator basis for the three‐cluster system is constructed. The indices of the reduction U(6)⊇U(2)×U(3) are chosen as the quantum numbers. The Pauli‐forbidden states are eliminated by the orthogonal transformation of basis functions. The basis states are obtained in terms of hypergeometric functions and the spherical Wigner functions. Their simple form allows one to solve the problem of calculating the matrix elements of the microscopic Hamiltonian needed for the study of three‐cluster systems within the algebraic version of RGM.

Recently Neil Ross and Peter Selinger analyzed the problem of approximating z- rotations by means of single-qubit Clifford+T circuits. Their main contribution is a deterministic-search technique which allowed them to make approximating circuits shallower. We adapt the deterministic-search technique to the case of Pauli+V circuits and prove similar results. Because of the relative simplicity of the Pauli+V framework, we use much simpler geometric methods., Comment: 27 pages, 3 figures

The theory of the algebras of Ignat’ev and Kuz’min and of Greenberg and Mohapatra is developed. These are algebras of inhibited parafermionic oscillators that describe possible small violations of the Pauli exclusion principle. The cyclic modules of the algebras are constructed so as to exhibit the connection of their fundamental properties, as uniqueness and statistical signature, with the relations in the algebras. The formalism is presented in such a way suited for further mathematical and physical developments, and has a natural continuation in a forthcoming paper.

The properties of the states Q(L1)1...Q(Ln)u( j,j), n≤N are investigated in a Lorentz rest frame; u(j,j) describes a massive one‐particle state of a maximal spin value j and a maximal spin projection j in a given field theoretical model; Q(L)A, A=1,2 stands for the Lth spinor charge, L=1,...,N, and N is the number of spinor charges appearing in the model. In particular, the concentration of this paper is on exploring the behavior of the before‐mentioned states under the action of the Pauli–Lubanski Casimir operator for the Poincare group and a discussion of the results so obtained is given.

The generalized Dyson boson mapping is extended to multifermion systems containing three‐particle substructures as occurring in nuclear matter. Two different approaches are described. The first one leads to a mapping involving equal numbers of bosons and fermions, where each boson, as usual, represents a fermion pair. The second possibility consists of the introduction of new kinds of fermions carrying the quantum numbers of the original three‐fermion subsystems. Both transformations are nonunitary.

An abstract asymptotic theory of a family of self-adjoint operators {Hκ}κ>0 acting in the tensor product of two Hilbert spaces is presented and it is applied to the nonrelativistic limit of the Pauli–Fierz model in quantum electrodynamics and of a spin-boson model. It is proven that the resolvent of Hκ converges strongly as κ→∞ and the limit is a pseudoresolvent, which defines an "effective operator" of Hκ at κ≈∞. As corollaries of this result, some limit theorems for Hκ are obtained, including a theorem on spectral concentration. An asymptotic estimate of the infimum of the spectrum (the ground state energy) of Hκ is also given. The application of the abstract theory to the above models yields some new rigorous results for them.

We construct lower bounds to the spectral gap of a family of Lindblad generators known as Davies maps. These maps describe the thermalization of quantum systems weakly coupled to a heat bath. The steady state of these systems is given by the Gibbs distribution with respect to the system Hamiltonian. The bounds can be evaluated explicitly, when the eigenbasis and the spectrum of the Hamiltonian is known. A crucial assumption is that the spectrum of the Hamiltonian is non-degenerate. Furthermore, we provide a counterexample to the conjecture, that the convergence rate is always determined by the gap of the associated Pauli master equation. We conclude, that the full dynamics of the Lindblad generator has to be considered. Finally, we present several physical example systems for which the bound to the spectral gap is evaluated., 24 pages, 5 figures

Integrable quantum mechanical systems for neutral particles with spin $\frac12$ and nontrivial dipole momentum are classified. It is demonstrated that such systems give rise to new exactly solvable problems of quantum mechanics with clear physical content. Solutions for three of them are given in explicit form. The related symmetry algebras and superalgebras are discussed. The presented classification is restricted to two-dimensional systems which admit matrix integrals of motion linear in momenta., 22 pages

In this paper we represent the generalization of relativistic quantum mechanics on the base of eght-component values "octons", generating associative noncommutative spatial algebra. It is shown that the octonic second-order equation for the eight-component octonic wave function, obtained from the Einshtein relation for energy and momentum, describes particles with spin of 1/2. It is established that the octonic wave function of a particle in the state with defined spin projection has the specific spatial structure in the form of octonic oscillator with two spatial polarizations: longitudinal linear and transversal circular. The relations between bispinor and octonic descriptions of relativistic particles are established. We propose the eight-component spinors, which are octonic generalisation of two-component Pauli spinors and four-component Dirac bispinors. It is shown that proposed eight-component spinors separate the states with different spin projection, different particle-antiparticle state as well as different polarization of the octonic oscillator. We demonstrate that in the frames of octonic relativistic quantum mechanics the second-order equation for octonic wave function can be reformulated in the form of the system of first-order equations for quantum fields, which is analogous to the system of Maxwell equations for the electromagnetic field. It is established that for the special type of wave functions the second-order equation can be reduced to the single first-order equation, which is analogous to the Dirac equation. At the same time it is shown that this first-order equation describes particles, which do not create quantum fields.

We construct the Pauli-Hamiltonian on a space where the position and momentum operators obey generalized commutation relations leading to the appearance of a minimal length. Using the momentum space representation we determine exactly the energy eigenvalues and eigenfunctions for a charged particle of spin half moving under the action of a constant magnetic field. The thermal properties of the system in the regime of high temperatures are also investigated, showing a magnetic behavior in terms of the minimal length.

Study of the normalizer of the MAD-group corresponding to a finegrading offers the most important tool for describing symmetries in the system of non-linear equations connected with contraction of a Lie algebra. One fine grading that is always present in any Lie algebra $sl(n,\mathbb{C})$ is the Pauli grading. The MAD-group corresponding to it is generated by generalized Pauli matrices. For such MAD-group, we already know its normalizer; its quotient group is isomorphic to the Lie group $Sl(2,\mathbb{Z}_n)\times v\mathbb{Z}_2$. In this paper, we deal with a more complicated situation, namely that the fine grading of $sl(p^2, \mathbb{C})$ is given by a tensor product of the Pauli matrices of the same order $p$, $p$ being a prime. We describe the normalizer of the corresponding MAD-group and we show that its quotient group is isomorphic to $Sp(4,\mathbb{Z}_p)\times\mathbb{Z}_2$.

The present paper is devoted to the detailed study of quantization and evolution of the point limit of the Pauli-Fierz model for a charged oscillator interacting with the electromagnetic field in dipole approximation. In particular, a well defined dynamics is constructed for the classical model, which is subsequently quantized according to the Segal scheme. To this end, the classical model in the point limit is reformulated as a second order abstract wave equation, and a consistent quantum evolution is given. This allows a study of the behaviour of the survival and transition amplitudes for the process of decay of the excited states of the charged particle, and the emission of photons in the decay process. In particular, for the survival amplitude the exact time behaviour is found. This is completely determined by the resonances of the systems plus a tail term prevailing in the asymptotic, long time regime. Moreover, the survival amplitude exhibites in a fairly clear way the Lamb shift correction to the unperturbed frequencies of the oscillator., Shortened version. To appear in J. Math. Phys

We consider a spin-1/2 charged particle in the plane under the influence of two idealized Aharonov-Bohm fluxes. We show that the Pauli operator as a differential operator is defined by appropriate boundary conditions at the two vortices. Further we explicitly construct a basis in the deficiency subspaces of the symmetric operator obtained by restricting the domain to functions with supports separated from the vortices. This construction makes it possible to apply the Krein's formula to the Pauli operator., LaTeX source file with 3 figures, to appear in JMP

We investigate the essential spectrum of the Pauli operators (and the Dirac and the Schrodinger operators) with magnetic fields on the Poincare upper-half plane. The magnetic fields under consideration are asymptotically constant (which may be equal to zero), or diverge at infinity. Moreover, the Aharonov–Casher type result is also considered.

A set of Feynman rules, similar to the rules of scalar electrodynamics, is derived for a full quantum electrodynamics based on the relativistic Klein–Gordon–type wave equation {ΠμΠμ+m2+ie σ ⋅ (C +iB)}φ =0, Πμ ≡−i ∂μ−eAμ, for spin‐ 1/2 particles [J. Math. Phys. 23, 1179 (1982); J. Math. Phys. 24, 2366 (1983)]. In this equation, φ is a 2×1 Pauli spinor and σa, a=1,2,3, are the usual 2×2 Pauli spin matrices. The irreducible self‐energy parts are compared to those of conventional quantum electrodynamics.

Pair correlated angular momentum projected standard Weyl tableau states spanning an m‐dimensional paired shell‐model space have been obtained for a system of 2N identical nucleons. A simple procedure has been developed for carrying out the restriction of the unitary group U(m) to the rotation group O(3) for configurations of both single and multilevel distributions of the single particle states. The mapping of the correlated pair configuration space onto the antisymmetric states allowed by Pauli principle is achieved using the particle antisymmetrizer. The procedure for determining the shell‐model Hamiltonian matrix using the above basis is outlined.

The quantum theory of particles of indefinite mass investigated earlier by Hostler [J. Math. Phys. 21, 2461 (1980); 22, 2307 (1981)] is adapted to apply to spin‐ 1/2 particles. The proposed wave equation is { 1/2 Π⋅(1+iσ)⋅Π+(1/i)(∂/∂λ)} φ=0, Πμ=pμ−eAμ, in which φ is a 2×1 Pauli spinor and σ is a spin tensor whose Lorentz components are 2×2 Pauli spin matrices. Particle scattering by an external c‐number static field is computed within the framework of the new formalism, and agreement with the known physics of a charged spin‐ 1/2 particle is obtained for this special case.

The Pauli–Schrodinger equation for a spin 1/2, neutral particle with a nonvanishing magnetic moment μ0, interacting with an external scalar potential V and a static magnetic field B, both functions of only one of the coordinates, is solved exactly for four different choices of the potential and the field. By choosing in the examples the coordinate y, we present these solutions in the following cases: (i) V( y)=0, B( y)=(B0sin κy, 0, B0cos κy) where B0 and κ are two arbitrary constants. (ii) V( y)=λ′y2, B( y)=‖αy‖(cos 2κy, 0, sin 2κy) where 6* λ=ℏ2/2m and α,κ arbitrary constants and λ′=λ(μ0/2κλ)2. (iii) V( y)=λ′(c1tan αy+c2cot αy)2, B( y)=B( y) (sin (2κy+2δ(y)), 0, cos (2κy+2δ( y)) where B2( y)=(c1tan αy+c2cot αy)2 (+α2/4κ2)(c1sec2αy−c2csc2αy)2 and tan 2δ( y)=(2κ/λ)((c1tan αy+c2cot αy) /(c1sec2αy−c2csc2αy)); c1, c2, α, and κ are arbitrary constants. (iv) V( y)=λ′(a tanh z+b)2 where z =[(y−cd)/d], B2( y)=(a tanh z+b)2+(a2/4κ2d2)sech2z, tan 2δ( y)=(2κd/a)((a tanh z+b)/sech2z); a, b, c, ...

Massless, D( j,0)⊕D(0, j), multispinor fields of arbitrary unmixed spin j are reduced by simple matrix‐algebra methods to associated tensors and tensor–spinors. A generalized Majorana condition applied to the multispinors is seen to correspond to reality and Majorana conditions on the associated tensors and tensor–spinors, respectively. The symmetries of the latter are displayed explicitly for arbitrary spin. For spin‐1, ‐ (3)/(2) , ‐2, and ‐ (5)/(2) the free‐field gauge‐invariant Lagrangian wave equations of Maxwell (spin‐1), Rarita–Schwinger (spin‐ (3)/(2) ), Fierz–Pauli (spin‐2), and spin‐ (5)/(2) are derived directly and in a uniform manner from the simpler equations of the unmixed spin reps strongly suggesting the method is extendable to arbitrary spin. Similar features of massive fields are briefly reviewed.

It is argued that the expression − KB Trace [〈ρ (t) 〉 ln〈ρ (t) 〉], which appears in a stochastic treatment of the dynamics of the density matrix is indeed the nonequilibrium entropy. The reasoning involves consideration of the time evolution of the free energy for a relaxing magnetic moment in a fluctuating magnetic environment. It is shown that the H theorem, and the monotonic decrease of the free energy, as described by Pauli’s master equation can be generalized to the full density matrix, at least for the case of magnetic relaxation, which requires the presence of off‐diagonal density matrix elements.

A theorem is presented on the location of the essential spectrum of certain intermediate Hamiltonians used to construct lower bounds to bound‐state energies of multiparticle atomic and molecular systems. This result is an analog of the Hunziker–Van Winter–Zhislin theorem for exact Hamiltonians, which implies that the continuum of an N‐electron system begins at the ground‐state energy for the corresponding system with N−1 electrons. The work presented here strengthens earlier results of Beattie [SIAM J. Math. Anal. 16, 492 (1985)] in that one may now consider Hamiltonians restricted to the symmetry subspaces appropriate to the permutational symmetry required by the Pauli exclusion principle, or to other physically relevant symmetry subspaces. The associated convergence theory is also given, guaranteeing that all bound‐state energies can be approximated from below with arbitrary accuracy.

Pauli master equation is derived rigorously in the framework of quantum stochastic processes.

A trial wavefunction of superconducting type is postulated for the ground state of a system of N positive and N negative charges with Coulomb interactions in the absence of any exclusion principle. The ground‐state binding energy is rigorously proved to be greater than AN75 Ry, where A is an absolute constant. Results of earlier perturbation‐theoretic calculations for an infinite system are confirmed. The author, with A. Lenard, has previously proved that the exclusion principle, holding for particles with one sign of charge only, is a sufficient condition for the stability of matter; the present paper shows that the exclusion principle is also necessary for stability.

The field equations for the Lee model are solved by constructing eigenfields from the most general possible combination of bare fermion and boson operators. These solutions are found to require an infinite number of boson terms, the coefficients of which obey the integral equations of scattering theory. It is discovered that the algebra of the Lee‐model fermion eigenfields is not that of free particle operators. The anticommutator of the ith fermion eigenfield Ai+ has the form {Ai, Ai+}+=1−Σj≠i Aj+ Aj, where the sum is over all other fermion eigenfields. An algebra of this type is not peculiar to the Lee model. It will hold for all fields which obey a general Pauli exclusion principle and which are orthogonal to one another. The explanation for this algebra lies in the fact that these eigenfields represent operators which create states and not particles. Several other models exhibiting this same behavior (including the harmonic oscillator) are presented; for these models boson fields may also be construct...

This paper considers the determination of N‐representability (for diagonal elements) of p‐density matrices restricted to certain finite‐dimensional subspaces of l2 of the configuration space of N identical antisymmetric particles. In particular, an arbitrary set of N + p spin orbitals is selected and one considers the (N+pp)‐dimensional subspace generated by all possible Slater determinants of the spin orbitals being considered. Applying a combinatorial approach to the problem, a necessary and sufficient set of conditions is determined; previous work has dealt only with necessary conditions, except in the 1‐matrix case. The paper concludes by presenting a probabilistic interpretation of these conditions which seems of particular interest for the 2‐matrix case. The conditions presented here in combination with the Pauli principle give a probabilistic view of the expected occupation of p‐tuples of spin orbitals in terms of the expected occupations of lower‐order‐tuples of spin orbitals.

A general theory of long range correlations in the ground state of a closed shell nucleus is outlined, using a number of ideas introduced or adumbrated, but not always successfully developed, in previous work of the authors and others. These include the following: (i) Any operator can be formally expressed as a series in particle‐hole (p‐h) excitation and destruction operators which should converge rapidly for a suitable choice of single‐particle basis at the closed shells. By means of these relations and with the help of sum rules all observables can be computed without the explicit use of wave functions. (ii) For a fixed choice of single‐particle basis, the ground state energy can be computed from a variational principle in which in lowest nontrivial approximation, in consequence of (i), the parameters are amplitudes of the same type as occur in the random phase approximation (RPA). The precise relation to RPA is fully detailed. (iii) The single particle basis chosen is the natural orbital basis of Lowdin, which presents itself as the obvious choice both for formulation of the dynamics and for the algorithm of solution. (iv) Though the theory deals with pairs of fermion operators, particular attention is paid that all Pauli principle restrictions are satisfied. (v) It is verified that in the perturbation limit, known results are reproduced. The method is generally applicable to any system for which the correlations can be viewed as particle‐hole excitations with respect to a reference Slater determinant.

Rigorous inequalities are derived for the ground‐state energy of a nonrelativistic quantum‐mechanical system of N particles in gravitational interaction. It is shown that gravitational forces do not saturate, the binding energy per particle increasing with N, like N2 for a Bose system, like (N4/3) for a Fermi system. As a by‐product, we obtain a generally valid Heisenberg‐like inequality for N‐fermion systems, expressing very simply the effect of the Pauli exclusion principle. These results are extended to the case of a system of oppositely charged particles which is shown to behave, with respect to gravitational forces, as a Fermi system as soon as particles with one sign of charge only are identical fermions. This explains quantitatively how and when gravitational forces finally predominate over Coulomb forces for large enough bodies (planets). A further extension to the case where relativistic effects enter only at the kinematical level permits us to derive rigorously from first principles the existence and an estimate of the Chandrasekhar mass limit, above which no collection of cold matter is stable (white dwarf stars).

We give the relevant solution to the integral equation which Kallen and Pauli have derived for elastic VΘ‐scattering in the Lee model. As an application of this result the exact Tamm‐Dancoff solution for the entire VΘ‐sector is obtained. This includes the amplitudes for VΘ‐ and N2Θ elastic scattering and VΘ‐N2Θ production, as well as their extensions off the mass shell.

The formalism of S‐operator theory is generalized to apply to all low‐spin particles with particular emphasis on quantum electrodynamics. It is shown that only direct (nongradient) interactions are allowed, when spinor fields are involved. The Pauli interaction is explicitly shown to be forbidden. Problems of gauge invariance are discussed and commutation rules between the interpolating quantum fields and ∂μAμin(X) are derived. Finite S‐matrix elements are easily calculated with complete convergence at each stage of the calculation.

A many‐body wavefunction is constructed by antisymmetrization, with respect to the electron variables, of a product of 4He‐atom wavefunctions, each in its individual ground state. This wavefunction is shown to have the following properties: (1) The pair distribution function D(Rij) vanishes at zero separation Rij = 0; part of the mutual repulsion of 4He atoms is built into the wavefunction as a result of the exclusion principle acting between the electron shells on different atoms. (2) Neither the nuclei nor the whole atoms undergo Bose condensation, but there is a ``Fermi condensation'' similar to that shown by Yang to characterize superconductivity, arising from off‐diagonal long‐range order of the appropriate reduced density matrix.

It is shown how the algebraic difficulties arising in some spin‐1 problems may be reduced to (almost) Pauli matix algebra.

It is shown that the existence of Aharonov–Bohm scattering depends upon the criteria used for establishing the stationary states. If one applies Pauli’s criterion, there is no scattering. It is shown further that applying the usual criteria that the wave functions be continuous and single valued, as was done by Aharonov and Bohm, leads to stationary state wave functions which, with two exceptions, are eigenstates of the acceleration operator corresponding to eigenvalue zero. The acceleration operator is undefined for the remaining two states. Thus, only the eigenfunctions satisfying the Pauli criterion lead to well‐defined, sensible physics.

In the framework of the Lagrangian field theory a new statistics for charged tensor fields is considered. An interaction Lagrangian is constructed such that the S–matrix is unitary, covariant and causal.