Related papers: Poisson Bracket for Fermion Fields: Correspondence…
We introduce and analyze a system of relativistic fermions in a space-time continuum, which interact via an action principle as previously considered in a discrete space-time. The model is defined by specifying the vacuum as a sum of Dirac…
A new approach to formulate the fermion field on lattice is introduced by proposing a new Dirac operator on lattice.This approach can eliminate the Fermion doubling problem, preserve the chiral symmetry and get the same dispersion relation…
Developing ideas based on combinatorial formulas for characteristic classes we introduce the algebra modeling secondary characteristic classes associated to $N$ connections. Certain elements of the algebra correspond to the ordinary and…
We study the Hamilton formalism for Connes-Lott models, i.e., for Yang-Mills theory in non-commutative geometry. The starting point is an associative $*$-algebra $\cA$ which is of the form $\cA=C(I,\cAs)$ where $\cAs$ is itself a…
Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…
One of the traditional ways of introducing bosons and fermions is through creation-annihilation algebras. Historically, these have been associated with emission and absorption processes at the quantum level and are characteristic of the…
We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…
We start from a Hamiltonian describing non-interacting fermions and add bosons to the model, with a Jaynes-Cummings-like interaction between the bosons and fermions. Because of the specific form of the interaction the model can be solved…
Constrained Hamiltonian systems fall into the realm of presymplectic geometry. We show, however, that also Poisson geometry is of use in this context. For the case that the constraints form a closed algebra, there are two natural Poisson…
We present a pseudoclassical mechanics model which exhibits gauge symmetry and time-reparametrization invariance. As such, first- and second-class constraints restrict the phase space, and the Hamiltonian weakly vanishes. We show that the…
The principle of invariance of the c-number symmetric bracket is used to derive both the quantum operator commutator relation $[\hat q, \hat p]=i\hbar$ and the time-dependent Schr\"odinger equation. A c-number dynamical equation is found…
It is shown that the Poisson bracket with boundary terms recently proposed by Bering (hep-th/9806249) can be deduced from the Poisson bracket proposed by the present author (hep-th/9305133) if one omits terms free of Euler-Lagrange…
The spin-statistics connection is obtained for a simple formulation of a classical field theory containing even and odd Grassmann variables. To that end, the construction of irreducible canonical realizations of the rotation group…
We investigate the semiclassical dynamics of massless Dirac fermions in 2+1 dimensions in the presence of external electromagnetic fields. By generalizing the $\alpha$ matrices to the spin-$S$ matrices and doing a certain scaling, we…
We present the Hamiltonian formulation of the bosonic Dirichlet p-brane action. We rewrite the recently proposed quadratic D-brane action in terms of generalized shift vector and lapse function. The first class and the second class…
We consider the application of the original Meyer-Miller (MM) Hamiltonian to mapping fermionic quantum dynamics to classical equations of motion. Non-interacting fermionic and bosonic systems share the same one-body density dynamics when…
In the case of two degree system the pairs of quadratic in momenta Hamiltonians commuting according the standard Poisson bracket are considered. The new many-parametrical families of such pairs are founded. The universal method of…
We introduce a family of compatible Poisson brackets on the space of $2\times 2$ polynomial matrices, which contains the reflection equation algebra bracket. Then we use it to derive a multi-Hamiltonian structure for a set of integrable…
This short note is devoted to the study of the Hamiltonian formalism and the integrability of the bosonic model introduced in [hep-th/0612079]. We calculate Poisson bracket of spatial components of Lax connection and we argue that its…
A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials is tested on the example of quantum electrodynamic fields produced by a…