59 research outputs found
Hamiltonization of theories with degenerate coordinates
We consider a class of Lagrangian theories where part of the coordinates does
not have any time derivatives in the Lagrange function (we call such
coordinates degenerate). We advocate that it is reasonable to reconsider the
conventional definition of singularity based on the usual Hessian and,
moreover, to simplify the conventional Hamiltonization procedure. In
particular, in such a procedure, it is not necessary to complete the degenerate
coordinates with the corresponding conjugate momenta.Comment: 14 pages, LaTex fil
Symmetries in Constrained Systems
As it is known, singular theories are theories with constraints in the Hamiltonian formulation. In particular, theories with first-class constraints are gauge theories.Qur aim is to describe symmetry structure of a general singular theory, and, in particular, to relate the structure of gauge transformations with the constraint structure
Dirac Equation in Noncommutative Space for Hydrogen Atom
We consider the energy levels of a hydrogen-like atom in the framework of
-modified, due to space noncommutativity, Dirac equation with Coulomb
field. It is shown that on the noncommutative (NC) space the degeneracy of the
levels and is lifted completely, such that new
transition channels are allowed.Comment: 9 pages, 1 figure; typos correcte
Gauge Symmetries on -Deformed Spaces
A Hamiltonian formulation of gauge symmetries on noncommutative (
deformed) spaces is discussed. Both cases- star deformed gauge transformation
with normal coproduct and undeformed gauge transformation with twisted
coproduct- are considered. While the structure of the gauge generator is
identical in either case, there is a difference in the computation of the
graded Poisson brackets that yield the gauge transformations. Our analysis
provides a novel interpretation of the twisted coproduct for gauge
transformations.Comment: LaTex, 20 pages, no figure
Particles with anomalous magnetic moment in external e.m. fields: the proper time formulation
In this paper we evaluate the expression for the Green function of a
pseudo-classical spinning particle interacting with constant electromagnetic
external fields by taking into account the anomalous magnetic and electric
moments of the particle. The spin degrees of freedom are described in terms of
Grassmann variables and the evolution operator is obtained through the
Fock-Schwinger proper time method.Comment: 10 page
Canonical quantization of so-called non-Lagrangian systems
We present an approach to the canonical quantization of systems with
equations of motion that are historically called non-Lagrangian equations. Our
viewpoint of this problem is the following: despite the fact that a set of
differential equations cannot be directly identified with a set of
Euler-Lagrange equations, one can reformulate such a set in an equivalent
first-order form which can always be treated as the Euler-Lagrange equations of
a certain action. We construct such an action explicitly. It turns out that in
the general case the hamiltonization and canonical quantization of such an
action are non-trivial problems, since the theory involves time-dependent
constraints. We adopt the general approach of hamiltonization and canonical
quantization for such theories (Gitman, Tyutin, 1990) to the case under
consideration. There exists an ambiguity (not reduced to a total time
derivative) in associating a Lagrange function with a given set of equations.
We present a complete description of this ambiguity. The proposed scheme is
applied to the quantization of a general quadratic theory. In addition, we
consider the quantization of a damped oscillator and of a radiating point-like
charge.Comment: 13 page
Quantization of the Damped Harmonic Oscillator Revisited
We return to the description of the damped harmonic oscillator by means of a
closed quantum theory with a general assessment of previous works, in
particular the Bateman-Caldirola-Kanai model and a new model recently proposed
by one of the authors. We show the local equivalence between the two models and
argue that latter has better high energy behavior and is naturally connected to
existing open-quantum-systems approaches.Comment: 16 page
Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action
It is known that actions of field theories on a noncommutative space-time can
be written as some modified (we call them -modified) classical actions
already on the commutative space-time (introducing a star product). Then the
quantization of such modified actions reproduces both space-time
noncommutativity and usual quantum mechanical features of the corresponding
field theory. The -modification for arbitrary finite-dimensional
nonrelativistic system was proposed by Deriglazov (2003). In the present
article, we discuss the problem of constructing -modified actions for
relativistic QM. We construct such actions for relativistic spinless and
spinning particles. The key idea is to extract -modified actions of the
relativistic particles from path integral representations of the corresponding
noncommtative field theory propagators. We consider Klein-Gordon and Dirac
equations for the causal propagators in such theories. Then we construct for
the propagators path-integral representations. Effective actions in such
representations we treat as -modified actions of the relativistic
particles. To confirm the interpretation, we quantize canonically these
actions. Thus, we obtain the Klein-Gordon and Dirac equations in the
noncommutative field theories. The -modified action of the relativistic
spinning particle is just a generalization of the Berezin-Marinov
pseudoclassical action for the noncommutative case
On Verification of the Non-Generational Conjectural- Derivation of First Class constraints: HP Monopole's Field case
In [7] we proposed a non-generational conjectural derivation of all first
class constraints (involving, only, variables compatible with canonical Poisson
brackets) for realistic gauge (singular) field theories; and we verified the
conjecture in cases of electromagnetic field, Yang Mills fields interacting
with scalar and spinor fields, and the gravitational field. Here we will
further verify our conjecture for the case of 't Hooft- Polyakov (HP)
monopole's field (i.e. in the Higgs Vacuum); and show that we will reproduce
the results in Ref.[6], which we reached at using Dirac's standard
multi-generational algorithm
Constraint algebra for Regge-Teitelboim formulation of gravity
We consider the formulation of the gravity theory first suggested by Regge
and Teitelboim where the space-time is a four-dimensional surface in a flat
ten-dimensional space. We investigate a canonical formalism for this theory
following the approach suggested by Regge and Teitelboim. Under constructing
the canonical formalism we impose additional constraints agreed with the
equations of motion. We obtain the exact form of the first-class constraint
algebra. We show that this algebra contains four constraints which form a
subalgebra (the ideal), and if these constraints are fulfilled, the algebra
becomes the constraint algebra of the Arnowitt-Deser-Misner formalism of
Einstein's gravity. The reasons for the existence of additional first-class
constraints in the canonical formalism are discussed.Comment: LaTeX, 12 pages; in this version the misprints in eq. (37) and (41)
was correcte
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