Probability representation and quantumness tests for qudits and two-mode light states

Using the tomographic-probability representation of spin states, the quantum behavior of qudits is examined. For a general j-qudit state, we propose an explicit formula for quantumness witness whose negative average value is incompatible with classical statistical model. The probability representations of quantum and classical (2j + 1)-level systems are compared within the framework of quantumness tests. In view of the Jordan–Schwinger map, the method is extended for checking the quantumness of two-mode light states.     

q$$ \bar q $$ pair production in non-Abelian gauge fields

We calculate the q pair production probability in the colour-flux tube model by considering the effect of non-Abelian interactions in the theory. Non-Abelian interactions in the colour field are time-dependent and hence should oscillate with a characteristic frequency ω ₀, which depends on the amplitude of the field strength. Using the WKB approximation in complex time, we calculated the pair production probability. When the strength of the field is comparable to the quark masses, the corresponding pair creation probability is maximum, and for the static field ω ₀ → 0, we recovered the well-known Schwinger result.      

Finite-Time Current Probabilities in the Asymmetric Exclusion Process on a Ring

We calculate the time-dependent probability distribution of current through a selected bond in the totally asymmetric exclusion process with periodic boundary conditions. We derive a general formula for the probability that the integrated current exceeds a given value N at the moment of time t. The formula is written in a form of a contour integral of a determinant of a Toeplitz matrix. Transforming the determinant expression, we obtain a generalization of the known formula derived by Johansson for the infinite one-dimensional lattice. To check the general formula, we consider the specific case corresponding to the probability of a minimal non-zero current. For this case we get an explicit analytical expression and analyze its asymptotics.     

反常、Chern-Simons上链

本文提出一种联络空间上同调的概念,建立这种上同调群与Chern-Simons型示性类系列的同态关系,给出它们在反常、Wess-Zumino有效作用与Schwinger项等问题上的应用;从而概括了Faddeev,宋行长,Zumino等人最近关于这些问题的探讨。 关键词：     

Particle creation by charged black holes

A simple derivation is given for the leading term (n=1) in the Schwinger formula for the pair creation by a constant electric field. The same approach is applied then to the charged particle production by a charged black hole. In this case, as distinct from that of a constant electric field, the probability of the charged particle production depends essentially on the particle energy. The production rate by black holes is found in the nonrelativistic and ultrarelativistic limits. The range of values for the mass and charge of a black hole is indicated where the discussed mechanism of radiation dominates the Hawking one.     

Correlation inequalities and the mass gap inP(φ)2

For theP()₂ field theory, we prove that the falloff of the (vacuum subtracted) two point Schwinger function dominates the higher order (vacuum subtracted) Schwinger functions. As applications, we prove that for even polynomials, the first excited state is odd, and that when there is a one particle state in the infinite volume limit, it is coupled to the vacuum by a single power of the field. The main inputs are the theory of Markov fields and the F.K.G. inequalities.     

Transformation theory ofq-quantum mechanics

Although there is no empirical motivation for replacing the commutators of dynamically conjugate operators in quantum mechanics byq-commutators, it appears possible to construct a consistent mathematical formulism based on this idea. To examine such a possibility further, we have studied the relation of this proposal to the Schwinger action principle, since the entire quantum mechanical formulism may be inferred from this principle. In particular, we have discussed the quantum transformation theory within this framework.To Julian Schwinger, 1918–1994, one of the creators of quantum field theory, and a giant of twentieth-century physics     

On “Schwinger mechanism for gluon pair production in?the?presence of arbitrary time dependent chromo-electric field”

Recently the paper “Schwinger mechanism for gluon pair production in the presence of arbitrary time dependent chromo-electric field” by G.C. Nayak was published [Eur. Phys. J. C 59:715, 2009; ]. Its aim is to obtain an exact expression for the probability of non-perturbative gluon pair production per unit time per unit volume and per unit transverse momentum in an arbitrary time-dependent chromo-electric background field. We believe that the obtained expression is open to question. We demonstrate its inconsistency on some well-known examples. We think that this is a consequence of using the so-called “shift theorem” [] in deriving the expression for the probability. We make some critical comments on the theorem and its applicability to the problem in question.     

On the axiomatic approach to quasi-classical field theory

We study the connection between quasi-classical field theory and axiomatic statements of the quantum field theory, Schwinger source theory, and the Lehmann-Symanzik-Zimmermann (LSZ) formalism. The classical Schwinger source is connected with the classical field; the LSZ R-function is connected with the quantum field operator. The axioms of the quantum field theory are written in the context of the quasi-classical expansion. In the considered approach, the stationary action principle and canonical commutation relations for field operators are obtained as corollaries and are not postulated as initial statements of the theory.     

New Exact Solution of Dirac-Coulomb Equation with Exact Boundary Condition

It usually writes the boundary condition of the wave equation in the Coulomb field as a rough form without considering the size of the atomic nucleus. The rough expression brings on that the solutions of the Klein-Gordon equation and the Dirac equation with the Coulomb potential are divergent at the origin of the coordinates, also the virtual energies, when the nuclear charges number Z>137, meaning the original solutions do not satisfy the conditions for determining solution. Any divergences of the wave functions also imply that the probability density of the meson or the electron would rapidly increase when they are closing to the atomic nucleus. What it predicts is not a truth that the atom in ground state would rapidly collapse to the neutron-like. We consider that the atomic nucleus has definite radius and write the exact boundary condition for the hydrogen and hydrogen-like atom, then newly solve the radial Dirac-Coulomb equation and obtain a new exact solution without any mathematical and physical difficulties. Unexpectedly, the K value constructed by Dirac is naturally written in the barrier width or the equivalent radius of the atomic nucleus in solving the Dirac equation with the exact boundary condition, and it is independent of the quantum energy. Without any divergent wave function and the virtual energies, we obtain a new formula of the energy levels that is different from the Dirac formula of the energy levels in the Coulomb field.     

Hamiltonian quantization of the non-anomalous generalized Schwinger model

We quantize a generalized version of the Schwinger model, where the two chiral sectors couples with different strengths to theU(1) gauge field. Starting from a theory which includes a generalized Wess-Zumino term, we obtain the equal time commutation relation for physical fields, both the singular and non-singular cases are considered. The photon propagators are also computed in their gauge dependent and invariant versions.     

Schwinger pair creation in multilayer graphene

The low energy effective field model for the multilayer graphene (at ABC stacking) in external Electric field is considered. The Schwinger pair creation rate and the vacuum persistence probability are calculated using the semiclassical approach.     

The scaling limit and Osterwalder-Schrader axioms for the two-dimensional Ising model

From a Feynman-Kac formula in a Fermion Fock space for the Schwinger functions of the infinite lattice periodic two-dimensional Ising model, scaled and scaling limit Schwinger functions are defined and shown to admit an absolutely convergent series representation. As the critical temperature is attained, it is shown that the scaled Schwinger functions converge and that the resulting scaling limit Schwinger functions obey the Osterwalder-Schrader axioms.     

Finite-Size Left-Passage Probability in Percolation

We obtain an exact finite-size expression for the probability that a percolation hull will touch the boundary, on a strip of finite width. In terms of clusters, this corresponds to the one-arm probability. Our calculation is based on the q-deformed Knizhnik–Zamolodchikov approach, and the results are expressed in terms of symplectic characters. In the large size limit, we recover the scaling behaviour predicted by Schramm’s left-passage formula. We also derive a general relation between the left-passage probability in the Fortuin–Kasteleyn cluster model and the magnetisation profile in the open XXZ chain with diagonal, complex boundary terms.     

No interactions for a collection of spin-two fields intermediated by a massive Rarita–Schwinger field

The cross-couplings among several massless spin-two fields (described in the free limit by a sum of Pauli–Fierz actions) in the presence of a massive Rarita–Schwinger field are investigated in the framework of the deformation theory based on local BRST cohomology. Under the hypotheses of locality, smoothness of the interactions in the coupling constant, Poincaré invariance, Lorentz covariance, and the preservation of the number of derivatives on each field, we prove that there are no consistent cross-interactions among different gravitons with a positively defined metric in internal space in the presence of a massive Rarita–Schwinger field. The basic features of the couplings between a single Pauli–Fierz field and a massive Rarita–Schwinger field are also emphasized.PACS 11.10.Ef     

Atomic coherent states as energy eigenstates of a Hamiltonian describing a two-dimensional anisotropic harmonic potential in a uniform magnetic field

In this paper we find that a set of energy eigenstates of a two-dimensional anisotropic harmonic potential in a uniform magnetic field is classified as the atomic coherent states |τ> in terms of the spin values of j in the Schwinger bosonic realization. The correctness of the above conclusions can be verified by virtue of the entangled state <η| representation of the state |τ>.     

Largest Terrestrial Electromagnetic Pulsar

The power spectrum formula of the synchrotron radiation generated by the electron and positron moving at the opposite angular velocities in homogenous magnetic field is derived in the Schwinger version of quantum field theory. It is surprising that the spectrum depends periodically on radiation frequency which means that the system composed from electron, positron, and magnetic field forms the pulsar.     

On the Gauge and BRST Invariance of the Chiral QED with Faddeevian Anomaly

Chiral Schwinger model with the Faddeevian anomaly is considered. It is found that imposing a chiral constraint this model can be expressed in terms of chiral boson. The model when expressed in terms of chiral boson remains anomalous and the Gauss law of which gives anomalous Poisson brackets between itself. In spite of that a systematic BRST quantization is possible. The Wess-Zumino term corresponding to this theory appears automatically during the process of quantization. A gauge invariant reformulation of this model is also constructed. Unlike the former one gauge invariance is done here without any extension of phase space. This gauge invariant version maps onto the vector Schwinger model. The gauge invariant version of the chiral Schwinger model for a=2 has a massive field with identical mass however gauge invariant version obtained here does not map on to that.     

Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD

The QCD vacuum condensates and various vacuum susceptibilities are all important parameters which characterize the nonperturbative properties of the QCD vacuum. In the QCD sum rules external field formula, various QCD vacuum susceptibilities play important roles in determining the properties of hadrons. In this paper, we review the recent progress in studies of vacuum susceptibilities together with their applications to the chiral phase transition of QCD. The results of the tensor, the vector, the axial–vector, the scalar, and the pseudo-scalar vacuum susceptibilities are shown in detail in the framework of Dyson–Schwinger equations.