562 research outputs found
Massive Spinning Particle in Any Dimension I. Integer Spins
The Kirillov-Souriau-Kostant construction is applied to derive the classical
and quantum mechanics for the massive spinning particle in arbitrary dimension.Comment: 13 pages, LaTe
BRST analysis of general mechanical systems
We study the groups of local BRST cohomology associated to the general
systems of ordinary differential equations, not necessarily Lagrangian or
Hamiltonian. Starting with the involutive normal form of the equations, we
explicitly compute certain cohomology groups having clear physical meaning.
These include the groups of global symmetries, conservation laws and Lagrange
structures. It is shown that the space of integrable Lagrange structures is
naturally isomorphic to the space of weak Poisson brackets. The last fact
allows one to establish a direct link between the path-integral quantization of
general not necessarily variational dynamics by means of Lagrange structures
and the deformation quantization of weak Poisson brackets.Comment: 38 pages, misprints corrected, references and the Conclusion adde
A uniform model of the massive spinning particle in any dimension
The general model of an arbitrary spin massive particle in any dimensional
space-time is derived on the basis of Kirillov - Kostant - Souriau approach. It
is shown that the model allows consistent coupling to an arbitrary background
of electromagnetic and gravitational fields.Comment: Latex, revised version of hep-th/981100
Quantizing non-Lagrangian gauge theories: an augmentation method
We discuss a recently proposed method of quantizing general non-Lagrangian
gauge theories. The method can be implemented in many different ways, in
particular, it can employ a conversion procedure that turns an original
non-Lagrangian field theory in dimensions into an equivalent Lagrangian
topological field theory in dimensions. The method involves, besides the
classical equations of motion, one more geometric ingredient called the
Lagrange anchor. Different Lagrange anchors result in different quantizations
of one and the same classical theory. Given the classical equations of motion
and Lagrange anchor as input data, a new procedure, called the augmentation, is
proposed to quantize non-Lagrangian dynamics. Within the augmentation
procedure, the originally non-Lagrangian theory is absorbed by a wider
Lagrangian theory on the same space-time manifold. The augmented theory is not
generally equivalent to the original one as it has more physical degrees of
freedom than the original theory. However, the extra degrees of freedom are
factorized out in a certain regular way both at classical and quantum levels.
The general techniques are exemplified by quantizing two non-Lagrangian models
of physical interest.Comment: 46 pages, minor correction
Radiation reaction and renormalization in classical electrodynamics of point particle in any dimension
The effective equations of motion for a point charged particle taking account
of radiation reaction are considered in various space-time dimensions. The
divergencies steaming from the pointness of the particle are studied and the
effective renormalization procedure is proposed encompassing uniformly the
cases of all even dimensions. It is shown that in any dimension the classical
electrodynamics is a renormalizable theory if not multiplicatively beyond d=4.
For the cases of three and six dimensions the covariant analogs of the
Lorentz-Dirac equation are explicitly derived.Comment: minor changes in concluding section, misprints corrected, LaTeX2e, 15
page
BRST theory without Hamiltonian and Lagrangian
We consider a generic gauge system, whose physical degrees of freedom are
obtained by restriction on a constraint surface followed by factorization with
respect to the action of gauge transformations; in so doing, no Hamiltonian
structure or action principle is supposed to exist. For such a generic gauge
system we construct a consistent BRST formulation, which includes the
conventional BV Lagrangian and BFV Hamiltonian schemes as particular cases. If
the original manifold carries a weak Poisson structure (a bivector field giving
rise to a Poisson bracket on the space of physical observables) the generic
gauge system is shown to admit deformation quantization by means of the
Kontsevich formality theorem. A sigma-model interpretation of this quantization
algorithm is briefly discussed.Comment: 19 pages, minor correction
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