763 research outputs found

### Algebraic and geometric aspects of generalized quantum dynamics

\noindent We briefly discuss some algebraic and geometric aspects of the
generalized Poisson bracket and non--commutative phase space for generalized
quantum dynamics, which are analogous to properties of the classical Poisson
bracket and ordinary symplectic structure.Comment: 10pages,revtex, IASSNSHEP-93/5

### Statistical thermodynamics for a non-commutative special relativity: Emergence of a generalized quantum dynamics

There ought to exist a description of quantum field theory which does not
depend on an external classical time. To achieve this goal, in a recent paper
we have proposed a non-commutative special relativity in which space-time and
matter degrees of freedom are treated as classical matrices with arbitrary
commutation relations, and a space-time line element is defined using a trace.
In the present paper, following the theory of Trace Dynamics, we construct a
statistical thermodynamics for the non-commutative special relativity, and show
that one arrives at a generalized quantum dynamics in which space and time are
non-classical and have an operator status. In a future work, we will show how
standard quantum theory on a classical space-time background is recovered from
here.Comment: 21 pages. arXiv admin note: text overlap with arXiv:1106.091

### Analytical results for the confinement mechanism in QCD_3

We present analytical methods for investigating the interaction of two heavy
quarks in QCD_3 using the effective action approach. Our findings result in
explicit expressions for the static potentials in QCD_3 for long and short
distances. With regard to confinement, our conclusion reflects many features
found in the more realistic world of QCD_4.Comment: 24 pages, uses REVTe

### Monte Carlo Quasi-Heatbath by approximate inversion

When sampling the distribution P(phi) ~ exp(-|A phi|^2), a global heatbath
normally proceeds by solving the linear system A phi = eta, where eta is a
normal Gaussian vector, exactly. This paper shows how to preserve the
distribution P(phi) while solving the linear system with arbitrarily low
accuracy. Generalizations are presented.Comment: 10 pages, 1 figure; typos corrected, reference added; version to
appear in Phys. Rev.

### Renormalization without infinities

Most renormalizable quantum field theories can be rephrased in terms of
Feynman diagrams that only contain dressed irreducible 2-, 3-, and 4-point
vertices. These irreducible vertices in turn can be solved from equations that
also only contain dressed irreducible vertices. The diagrams and equations that
one ends up with do not contain any ultraviolet divergences. The original bare
Lagrangian of the theory only enters in terms of freely adjustable integration
constants. It is explained how the procedure proposed here is related to the
renormalization group equations. The procedure requires the identification of
unambiguous "paths" in a Feynman diagrams, and it is shown how to define such
paths in most of the quantum field theories that are in use today. We do not
claim to have a more convenient calculational scheme here, but rather a scheme
that allows for a better conceptual understanding of ultraviolet infinities.
Dedicated to Paul Frampton's 60th birthdayComment: 8 pages, 11 figures. Proc. Coral Gables Conference, dec. 16-21, 200

### Weisskopf-Wigner Decay Theory for the Energy-Driven Stochastic Schr\"odinger Equation

We generalize the Weisskopf-Wigner theory for the line shape and transition
rates of decaying states to the case of the energy-driven stochastic
Schr\"odinger equation that has been used as a phenomenology for state vector
reduction. Within the standard approximations used in the Weisskopf-Wigner
analysis, and assuming that the perturbing potential inducing the decay has
vanishing matrix elements within the degenerate manifold containing the
decaying state, the stochastic Schr\"odinger equation linearizes. Solving the
linearized equations, we find no change from the standard analysis in the line
shape or the transition rate per unit time. The only effect of the stochastic
terms is to alter the early time transient behavior of the decay, in a way that
eliminates the quantum Zeno effect. We apply our results to estimate
experimental bounds on the parameter governing the stochastic effects.Comment: 29 pages in RevTeX, Added Note, references adde

### On Di\'osi-Penrose criterion of gravity-induced quantum collapse

It is shown that the Di\'osi-Penrose criterion of gravity-induced quantum
collapse may be inconsistent with the discreteness of space-time, which is
generally considered as an indispensable element in a complete theory of
quantum gravity. Moreover, the analysis also suggests that the discreteness of
space-time may result in rapider collapse of the superposition of energy
eigenstates than required by the Di\'osi-Penrose criterion.Comment: 5 pages, no figure

### Master Functional And Proper Formalism For Quantum Gauge Field Theory

We develop a general field-covariant approach to quantum gauge theories.
Extending the usual set of integrated fields and external sources to "proper"
fields and sources, which include partners of the composite fields, we define
the master functional Omega, which collects one-particle irreducible diagrams
and upgrades the usual Gamma-functional in several respects. The functional
Omega is determined from its classical limit applying the usual diagrammatic
rules to the proper fields. Moreover, it behaves as a scalar under the most
general perturbative field redefinitions, which can be expressed as linear
transformations of the proper fields. We extend the Batalin-Vilkovisky
formalism and the master equation. The master functional satisfies the extended
master equation and behaves as a scalar under canonical transformations. The
most general perturbative field redefinitions and changes of gauge-fixing can
be encoded in proper canonical transformations, which are linear and do not mix
integrated fields and external sources. Therefore, they can be applied as true
changes of variables in the functional integral, instead of mere replacements
of integrands. This property overcomes a major difficulty of the functional
Gamma. Finally, the new approach allows us to prove the renormalizability of
gauge theories in a general field-covariant setting. We generalize known
cohomological theorems to the master functional and show that when there are no
gauge anomalies all divergences can be subtracted by means of parameter
redefinitions and proper canonical transformations.Comment: 32 pages; v2: minor changes and proof corrections, EPJ

### Matter-induced vertices for photon splitting in a weakly magnetized plasma

We evaluate the three-photon vertex functions at order $B$ and $B^{2}$ in a
weak constant magnetic field at finite temperature and density with on shell
external lines. Their application to the study of the photon splitting process
leads to consider high energy photons whose dispersion relations are not
changed significantly by the plasma effects. The absorption coefficient is
computed and compared with the perturbative vacuum result. For the values of
temperature and density of some astrophysical objects with a weak magnetic
field, the matter effects are negligible.Comment: 14 pages, 1 figure. Accepted for publication in PR

- …