Related papers: Constraint Reorganization Consistent with the Dira…
The split involution quantization scheme, proposed previously for pure second--class constraints only, is extended to cover the case of the presence of irreducible first--class constraints. The explicit Sp(2)--symmetry property of the…
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
A toy model (suggested by Klauder) is analyzed from the perspective of First Class and Second Class Dirac constrained systems. The comparison is made by turning a First Class into a Second Class system with the introduction of suitable…
We extend Hamilton-Jacobi theory to Lagrange-Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians as well as holonomic and nonholonomic constraints. We refer…
We present a detailed analysis of the Hamiltonian constraints of the d-dimensional tetrad-connection gravity where the non-dynamical part of the spatial connection is fixed to zero by an adequate guage transformation. This new action…
In this paper, the Hamiltonian structure of the bosonized chiral Schwinger model (BCSM) is analyzed. From the consistency condition of the constraints obtained from the Dirac method, we can observe that this model presents, for certain…
Chord diagrams and combinatorics of word algebras are used to model products of Dirac matrices, their traces, and contractions. A simple formula for the result of arbitrary contractions is derived, simplifying and extending an old…
We investigate refined algebraic quantisation within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling a momentum-type constraint. The quantum constraint is implemented by a…
We perform the full Hamiltonian analysis of the topological BFCG action based on the Poincare 2-group. The Hamiltonian of the theory is constructed, and the algebra of constraints is computed. The Dirac brackets are evaluated, and the…
Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical…
Starting from a Lagrangian we perform the full constraint analysis of the Hamiltonian for General relativity in the tetrad-connection formulation for an arbitrary value of the Immirzi parameter and solve the second class constraints,…
A generalized version is proposed for the field-antifield formalism. The antibracket operation is defined in arbitrary field-antifield coordinates. The antisymplectic definitions are given for first- and second-class constraints. In the…
Dirac notation is widely used in quantum physics and quantum programming languages to define, compute and reason about quantum states. This paper considers Dirac notation from the perspective of automated reasoning. We prove two main…
In the present article, using a further generalization of the algebraic method of separation of variables, the Dirac equation is separated in a family of space-times where it is not possible to find a complete set of first order commuting…
First class constraints in a canonical formalism of a gauge theory might generate transformations which map a state to its physically equivalent state. This is called Dirac's conjecture. There are two examples which may be candidates of…
For interacting classical field theories such as general relativity exact solutions typically can only be found by imposing physically motivated (Killing) {\it symmetry} assumptions. Such highly symmetric solutions are then often used as…
We describe symmetry structure of a general singular theory (theory with constraints in the Hamiltonian formulation), and, in particular, we relate the structure of gauge transformations with the constraint structure. We show that any…
Second order degenerate Cl\`ement and Sar{\i}o\u{g}lu-Tekin Lagrangians are casted into forms of various first order Lagrangians. Hamiltonian analysis of these equivalent formalisms are performed by means of Dirac-Bergmann constraint…
We apply the Dirac procedure for constrained systems to the Arnowitt-Deser-Misner formalism linearized around the Bianchi I universe. We discuss and employ basic concepts such as Dirac observables, Dirac brackets, gauge-fixing conditions,…
In the Hamiltonian formalism, and in the presence of a symmetry Lie group, a variational reduction procedure has already been developed for Hamiltonian systems without constraints. In this paper we present a procedure of the same kind, but…