335 research outputs found
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.Comment: 8 page
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 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 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.Comment: 16 pages, RevTex, no figures, A few typewritten errors have been
correcte
Spinor and Isospinor Structure of Relativistic Particle Propagators
Representations by means of path integrals are used to find spinor and
isospinor structure of relativistic particle propagators in external fields.
For Dirac propagator in an external electromagnetic field all grassmannian
integrations are performed and a general result is presented via a bosonic path
integral. The spinor structure of the integrand is given explicitly by its
decomposition in the independent -matrix structures. Similar technique
is used to get the isospinor structure of the scalar particle propagator in an
external non-Abelian field.Comment: 9 pages, Preprint IC/93/197 Triest
PCT, spin and statistics, and analytic wave front set
A new, more general derivation of the spin-statistics and PCT theorems is
presented. It uses the notion of the analytic wave front set of
(ultra)distributions and, in contrast to the usual approach, covers nonlocal
quantum fields. The fields are defined as generalized functions with test
functions of compact support in momentum space. The vacuum expectation values
are thereby admitted to be arbitrarily singular in their space-time dependence.
The local commutativity condition is replaced by an asymptotic commutativity
condition, which develops generalizations of the microcausality axiom
previously proposed.Comment: LaTeX, 23 pages, no figures. This version is identical to the
original published paper, but with corrected typos and slight improvements in
the exposition. The proof of Theorem 5 stated in the paper has been published
in J. Math. Phys. 45 (2004) 1944-195
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
, where . 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 K\"{a}llen-Lehmann is proposed. It is applicable to any initial and
final string configurations and manifests exponential growth of spectral
densities intrinsic in nonlocalizable theories.Comment: This version is identical to the initial one whose ps and pdf files
were unavailable, with few corrections of misprint
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.Comment: 13 pages, LaTex file, one figure (not included
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