arXiv subjects

V. Ya. Fainberg

Publications and source records attributed to V. Ya. Fainberg.

10 recordsLinked to original sources

arXiv2005

Equivalence of Many-Gluon Green Functions in Duffin-Kemmer-Petieu and Klein-Gordon-Fock Statistical Quantum Field Theories

We prove the equivalence of many-gluon Green functions in Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories. The proof is based on the functional integral formulation for the statistical generating functional in a finite-temperature quantum field theory. As an illustration, we calculate one-loop polarization operators in both theories and show that their expressions indeed coincide.

nlin.SI↗

arXiv2003

Bose-Einstein Condensation and Free DKP field

The thermodynamical partition function of the Duffin-Kemmer-Petiau theory is evaluated using the imaginary-time formalism of quantum field theory at finite temperature and path integral methods. The DKP partition function displays two features: (i) full equivalence with the partition function for charged scalar particles and charged massive spin 1 particles; and (ii) the zero mode sector which is essential to reproduce the well-known relativistic Bose-Einstein condensation for both theories.

hep-th↗

arXiv2003

Equivalence of Many-Photon Green Functions in DKP and KGF Statistical Quantum Field Theories

We prove the equivalence of many-photon Green functions in statistical quantum field Duffin-Kemmer-Petiau (DKP) and Klein-Gordon-Fock (KGF) theories using functional path integral formalism for partition functional in statistical quantum (finite temperature) field theory. We also calculate the polarization operators in these theories in one-loop approximation, and demonstrate their coincidence.

hep-th↗

arXiv2003

Massless DKP fields in Riemann-Cartan space-times

We study massless Duffin-Kemmer-Petiau (DKP) fields in the context of Einstein-Cartan gravitation theory, interacting via minimal coupling procedure. In the case of an identically vanishing torsion (Riemannian space-times) we show that there exists local gauge symmetries which reproduce the usual gauge symmetries for the massless scalar and electromagnetic fields. On the other hand, similarly to what happens with the Maxwell theory, a non-vanishing torsion, in general, breaks the usual U(1) local gauge symmetry of the electromagnetic field or, in a different point of view, impose conditions on the torsion.

gr-qc↗

arXiv2002

Non-Localizability and Asymptotic Commutativity

The mathematical formalism commonly used in treating nonlocal highly singular interactions is revised. The notion of support cone is introduced which replaces that of support for nonlocalizable distributions. Such support cones are proven to exist for distributions defined on the Gelfand-Shilov spaces $S^β$, where $0<β<1$ . This result leads to a refinement of previous generalizations of the local commutativity condition to nonlocal quantum fields. For string propagators, a new derivation of a representation similar to that of Källen-Lehmann is proposed. It is applicable to any initial and final string configurations and manifests exponential growth of spectral densities intrinsic in nonlocalizable theories.

hep-th↗

arXiv2000

Duffin-Kemmer-Petiau and Klein-Gordon-Fock Equations for Electromagnetic, Yang-Mills and external Gravitational Field Interactions: proof of equivalence

Starting from Generating functional for Green Function (GF), constracted from Lagrangian action in Duffin-Kemmer-Petiau (DKP) theory (L-approach) we strictly prove that the physical matrix elements of S-matrix in DKP and Klein-Gordon-Fock (KGF) theories coincide in cases of interaction spin O particles with external and quantized Maxwell and Yang-Mills fields and in case of external gravitational field (without or with torsion). For the proof we use reduction formulas of Lehmann Symanzik, Zimmermann (LSZ). We prove that many photons and Yang-Mills particles GF coincide in the both theories, too.

hep-th↗

arXiv1999

On Equivalence of Duffin-Kemmer-Petiau and Klein-Gordon Equations

A strict proof of equivalence between Duffin-Kemmer-Petiau (DKP) and Klein-Gordon (KG) theories is presented for physical S-matrix elements in the case of charged scalar particles interacting in minimal way with an external or quantized electromagnetic field. First, Hamiltonian canonical approach to DKP theory is developed in both component and matrix form. The theory is then quantized through the construction of the generating functional for Green functions (GF) and the physical matrix elements of S-matrix are proved to be relativistic invariants. The equivalence between both theories is then proved using the connection between GF and the elements of S-matrix, including the case of only many photons states, and for more general conditions - so called reduction formulas of Lehmann, Symanzik, Zimmermann.

hep-th↗

arXiv1997

On Quantum Corrections to Chern-Simons Spinor Electrodynamics

We make a detailed investigation on the quantum corrections to Chern-Simons spinor electrodynamics. Starting from Chern-Simons spinor quantum electrodynamics with the Maxwell term $-1/(4γ){\int}d^3x F_{μν}F^{μν}$ and by calculating the vacuum polarization tensor, electron self-energy and on-shell vertex, we explicitly show that the Ward identity is satisfied and hence verify that the physical quantities are independent of the procedure of taking $γ{\to}{\infty}$ at one-loop and tree levels. In particular, we find the three-dimensional analogue of the Schwinger anomalous magnetic moment term of the electron produced from the quantum corrections.

hep-th↗

arXiv1996

The Path Integral Quantization And The Construction Of The S-matrix In The Abelian And Non-Abelian Chern-Simons Theories

The cvariant path integral quantization of the theory of the scalar and spinor particles interacting through the abelian and non-Abelian Chern-Simons gauge fields is carried out and is shown to be mathematically ill defined due to the absence of the transverse components of these gauge fields. This is remedied by the introduction of the Maxwell or the Maxwell-type (in the non-Abelian case)term which makes the theory superrenormalizable and guarantees its gauge-invariant regularization and renormalization. The generating functionals are constructed and shown to be formally the same as those of QED (or QCD) in 2+1 dimensions with the substitution of the Chern-Simons propagator for the photon (gluon) propagator. By constructing the propagator in the general case, the existence of two limits; pure Chern-Simons and QED (QCD) after renormalization is demonstrated. By carrying out carefully the path integral quantization of the non-Abelian Chern-Simons theories using the De Witt-Fadeev-Popov and the Batalin-Fradkin- Vilkovisky methods it is demonstrated that there is no need to quantize the dimensionless charge of the theory. The main reason is that the action in the exponent of the path integral is BRST-invariant which acquires a zero winding number and guarantees the BRST renormalizability of the model. The S-matrix operator is constructed, and starting from this S-matrix operator novel topological unitarity identities are derived that demand the vanishing of the gauge-invariant sum of the imaginary parts of the Feynman diagrams with a given number of intermediate on-shell topological photon lines in each order of perturbation theory. These identities are illustrated by an explicit example.

hep-th↗

arXiv1995

The Topological Unitarity Identities in Chern-Simons Theories

Starting from the generating functional of the theory of relativistic spinors in 2+1 dimensions interacting through the pure Chern-Simons gauge field, the S-matrix is constructed and seen to be formally the same as that of spinor quantum electrodynamics in 2+1 dimensions with Feynman diagrams having external photon lines excluded, and with the propagator of the topological Chern-Simons photon substituted for the Maxwell photon propagator. It is shown that the absence of real topological photons in the complete set of vector states of the total Hilbert space leads in a given order of perturbation theory to topological unitarity identities that demand the vanishing of the gauge-invariant sum of the imaginary parts of Feynman diagrams with a given number of internal on-shell free topological photon lines. It is also shown, that these identities can be derived outside the framework of perturbation theory. The identities are verified explicitly for the scattering of a fermion-antifermion pair in one-loop order.

hep-th↗