相关论文: On the constrained structure of duality symmetric …

The Hamiltonian formalism is extremely elegant and convenient to mechanics problems. However, its application to the classical field theories is a difficult task. In fact, you can set one to one correspondence between the Lagrangian and…

The dynamical systems invariant under gauge transformations with higher order time derivatives of the gauge parameter are considered from the Hamiltonian point of view. We investigate the consequences of the basic requirements that the…

Dirac's quantization of the Maxwell theory on non-commutative spaces has been considered. First class constraints were found which are the same as in classical electrodynamics. The gauge covariant quantization of the non-linear equations of…

In this paper, we discuss Galilean relativistic Maxwell theory in detail. We first provide a set of mapping relations, derived systematically, that connect the covariant and contravariant vectors in the Lorentz relativistic and Galilean…

The most common physical formalisms are the Lagrangian formalism and the Hamiltonian formalism. From the superficial point of view, they are one and the same, but rewritten in other terms. However, it seems that the Hamiltonian formalism…

Dirac algorithm allows to construct Hamiltonian systems for singular systems, and so contributing to its successful quantization. A drawback of this method is that the resulting quantized theory does not have manifest Lorentz invariance.…

The WDVV equations of associativity in 2-d topological field theory are completely integrable third order Monge-Amp\`ere equations which admit bi-Hamiltonian structure. The time variable plays a distinguished role in the discussion of…

We consider Maxwell theory on a non-spin manifold. Depending on the choice of statistics for line operators, there are three non-anomalous theories and one anomalous theory with different symmetry fractionalizations. We establish the…

It is shown that the Dirac approach to Hamiltonization of singular theories can be slightly modified in such a way that primary Dirac constraints do not appear in the process. According to the modified scheme, Hamiltonian formulation of…

We provide an explicit construction of a manifestly duality invariant, interacting deformation of Maxwell theory in four dimensions in terms of mutually local, but interacting 1- and 3-forms. Interestingly, our theory is formulated directly…

Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L2 duality, and one utilizing an abstract notion of duality. The final of…

Classes of relativistic symmetries accommodating supersymmetric patterns are considered for the Dirac Hamiltonian with axially-deformed scalar and vector potentials.

We describe the interplay between electric-magnetic duality and higher symmetry in Maxwell theory. When the fine-structure constant is rational, the theory admits non-invertible symmetries which can be realized as composites of…

We find the dual equivalent (gauge invariant) version of the Maxwell theory in D=4 with a Proca-like mass term by using the symplectic embedding method. The dual theory obtained (Maxwell-Podolsky) includes a higher-order derivative term and…

A natural and very important development of constrained system theory is a detail study of the relation between the constraint structure in the Hamiltonian formulation with specific features of the theory in the Lagrangian formulation,…

A new Hamiltonian structure of the Maxwell-Bloch equations is described. In this setting the Maxwell-Bloch equations appear as a member of a family of generalized Maxwell-Bloch systems. The family is parameterized by compact semi-simple Lie…

Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…

We develop a complete Dirac's canonical analysis for an alternative action that yields Maxwell's four-dimensional equations of motion. We study in detail the full symmetries of the action by following all steps of Dirac's method in order to…

The main goal of these lectures is to introduce and review the Hamiltonian formalism for classical constrained systems and in particular gauge theories. Emphasis is put on the relation between local symmetries and constraints and on the…

A detailed Dirac's canonical analysis for a topological four dimensional $BF$-like theory with a compact dimension is developed. By performing the compactification process we find out the relevant symmetries of the theory, namely, the full…