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- W1600000012 abstract "Applied to field theory, the familiar symplectic technique leads to instantaneous Hamiltonian formalism on an infinite-dimensional phase space. A true Hamiltonian partner of first order Lagrangian theory on fibre bundles $Yto X$ is covariant Hamiltonian formalism in different variants, where momenta correspond to derivatives of fields relative to all coordinates on $X$. We follow polysymplectic (PS) Hamiltonian formalism on a Legendre bundle over $Y$ provided with a polysymplectic $TX$-valued form. If $X=mathbb R$, this is a case of time-dependent non-relativistic mechanics. PS Hamiltonian formalism is equivalent to the Lagrangian one if Lagrangians are hyperregular. A non-regular Lagrangian however leads to constraints and requires a set of associated Hamiltonians. We state comprehensive relations between Lagrangian and PS Hamiltonian theories in a case of semiregular and almost regular Lagrangians. Quadratic Lagrangian and PS Hamiltonian systems, e.g. Yang - Mills gauge theory are studied in detail. Quantum PS Hamiltonian field theory can be developed in the frameworks both of familiar functional integral quantization and quantization of the PS bracket." @default.
- W1600000012 created "2016-06-24" @default.
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- W1600000012 date "2015-05-06" @default.
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- W1600000012 title "Polysymplectic Hamiltonian Field Theory" @default.
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