Related papers: Canonical and D-transformations in Theories with C…
A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
Canonical transformation in a three-dimensional phase space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed as based on canonoid transformations. It is shown that…
This paper presents the general theory of canonical transformations of coordinates in quantum mechanics. First, the theory is developed in the formalism of phase space quantum mechanics. It is shown that by transforming a star-product, when…
A theory of non-unitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. That all quantum canonical transformations without an explicit $\hbar$ dependence are also…
We complete the process of classifying all supersymmetric theories with quantum modified moduli. We present all the supersymmetric gauge theories based on a simple orthogonal or exceptional group that exhibit a quantum modified moduli…
We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric forms of trajectories are associated with different integrals…
Quantum canonical transformations are defined in analogy to classical canonical transformations as changes of the phase space variables which preserve the Dirac bracket structure. In themselves, they are neither unitary nor non-unitary. A…
In a classical Hamiltonian theory with second class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in…
In this paper, I consider a recent controversy about whether first-class constraints generate gauge transformations in the case of electromagnetism. I argue that there is a notion of gauge transformation, the extended notion, which is…
Parametrized field theories, which are generally covariant versions of ordinary field theories, are studied from the point of view of the covariant phase space: the space of solutions of the field equations equipped with a canonical…
We show that S-duality in four dimensional non-supersymmetric abelian gauge theories can be formulated as a canonical transformation in the phase space of the theory. This transformation is the usual interchange between electric and…
A new kind of deformed calculus (the D-deformed calculus) that takes place in fractional-dimensional spaces is presented. The D-deformed calculus is shown to be an appropriate tool for treating fractional-dimensional systems in a simple way…
D-theory is an alternative non-perturbative approach to quantum field theory formulated in terms of discrete quantized variables instead of classical fields. Classical scalar fields are replaced by generalized quantum spins and classical…
Vertex algebras in higher dimensions correspond to models of quantum field theory with global conformal invariance. Any vertex algebra in dimension D admits a restriction to a vertex algebra in any lower dimension and, in particular, to…
For a certain example of a "doubly special relativity theory" the modified space-time Lorentz transformations are obtained from momentum space transformations by using canonical methods. In the sequel an energy-momentum dependent space-time…
We show that any theory with second class constraints may be cast into a gauge theory if one makes use of solutions of the constraints expressed in terms of the coordinates of the original phase space. We perform a Lagrangian path integral…
We begin the process of classifying all supersymmetric theories with quantum modified moduli. We determine all theories based on a single SU or Sp gauge group with quantum modified moduli. By flowing among theories we have calculated the…
This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial…
We consider a higher-derivative generalization of disformal transformations in $D$-dimensional spacetime and clarify the conditions under which they form a group with respect to the matrix product and the functional composition. These…