557 research outputs found
Covariant Hamiltonian field theory. Path integral quantization
The Hamiltonian counterpart of classical Lagrangian field theory is covariant
Hamiltonian field theory where momenta correspond to derivatives of fields with
respect to all world coordinates. In particular, classical Lagrangian and
covariant Hamiltonian field theories are equivalent in the case of a
hyperregular Lagrangian, and they are quasi-equivalent if a Lagrangian is
almost-regular. In order to quantize covariant Hamiltonian field theory, one
usually attempts to construct and quantize a multisymplectic generalization of
the Poisson bracket. In the present work, the path integral quantization of
covariant Hamiltonian field theory is suggested. We use the fact that a
covariant Hamiltonian field system is equivalent to a certain Lagrangian system
on a phase space which is quantized in the framework of perturbative field
theory. We show that, in the case of almost-regular quadratic Lagrangians, path
integral quantizations of associated Lagrangian and Hamiltonian field theories
are equivalent.Comment: 18 p
The KT-BRST complex of a degenerate Lagrangian system
Quantization of a Lagrangian field system essentially depends on its
degeneracy and implies its BRST extension defined by sets of non-trivial
Noether and higher-stage Noether identities. However, one meets a problem how
to select trivial and non-trivial higher-stage Noether identities. We show
that, under certain conditions, one can associate to a degenerate Lagrangian L
the KT-BRST complex of fields, antifields and ghosts whose boundary and
coboundary operators provide all non-trivial Noether identities and gauge
symmetries of L. In this case, L can be extended to a proper solution of the
master equation.Comment: 15 pages, accepted for publication in Lett. Math. Phy
BV quantization of covariant (polysymplectic) Hamiltonian field theory
Covariant (polysymplectic)Hamiltonian field theory is the Hamiltonian
counterpart of classical Lagrangian field theory. They are quasi-equivalent in
the case of almost-regular Lagrangians. This work addresses BV quantization of
polysymplectic Hamiltonian field theory. We compare BV quantizations of
associated Lagrangian and polysymplectic Hamiltonian field systems in the case
of almost-regular quadratic Lagrangians.Comment: 24 page
- …