Related papers: Classical Mechanics and kappa-symmetry
In a recent paper we have analyzed the role that a universal set of local symmetries plays in suppressing the superposition principle in classical mechanics via a path-integral formulation of classical mechanics itself. In this paper first…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
Koopman-von Neumann in the 30's gave an operatorial formululation of Classical Mechanics. It was shown later on that this formulation could also be written in a path-integral form. We will label this functional approach as CPI (for…
We present the quantum and classical mechanics formalisms for a particle with position-dependent mass in the context of a deformed algebraic structure (named $\kappa$-algebra), motivated by the Kappa-statistics. From this structure we…
We perform canonical analysis of non-relativistic particle in Newton-Cartan Background. Then we extend this analysis to the case of non-relativistic superparticle in the same background. We determine constraints structure of this theory and…
We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion…
In this paper we show that, via an extension of time, some metric structures naturally appear in both classical and quantum mechanics when both are formulated via path integrals. We calculate the various Ricci scalar and curvatures…
We reformulate Classical Mechanics as a timeless relativistic theory. Readers are introduced to a new class of reference systems, the binate frames, where physical events are identified with four position-coordinates -- no clocks are used.…
A generalization of the notion of a (pseudo-) Riemannian space is proposed in a framework of noncommutative geometry. In particular, there are parametrized families of generalized Riemannian spaces which are deformations of classical…
Pairs $\aa \subset \bb$ of local quantum field theories are studied, where $\aa$ is a chiral conformal \qft and $\bb$ is a local extension, either chiral or two-dimensional. The local correlation functions of fields from $\bb$ have an…
The arising of central extensions is discussed in two contexts. At first classical counterparts of quantum anomalies (deserving being named as "classical anomalies") are associated with a peculiar subclass of the non-equivariant maps.…
Classical and quantum mechanics for an extended Heisenberg algebra with canonical commutation relations for position and momentum coordinates are considered. In this approach additional noncommutativity is removed from the algebra by linear…
In this article one introduces a formalism of classical mechanics where complex Lagrangian functions are admitted. The results include complex versions of the Lagrangian function, of the Euler-Lagrange equation, of the Hamilton principle, a…
We show how the Bell correlations can be modelled locally by relaxing the joint probability relation for independent variables $P(a,b)=P(a)P(b)$ outside classical settings, with complex/quaternion generators for the measurement outcomes…
We establish the correspondence between two apparently unrelated but in fact complementary approaches of a relativistic deformed kinematics: the geometric properties of momentum space and the loss of absolute locality in canonical…
We prove a compactness result with respect to $\Gamma$-convergence for a class of integral functionals which are expressed as a sum of a local and a non-local term. The main feature is that, under our hypotheses, the local part of the…
This work constitutes the second part of a series of studies that aim to utilise tools from Hamiltonian mechanics to investigate the motion of an extended body in general relativity. The first part of this work [Refs. [1, 2]] constructed a…
We first provide a classical analysis proof of a version of the Alexandroff-Bakelman-Pucci inequality (ABP) for compactly supported $C^2$ functions in dimension $2$, inspired by the symplectic geometry proof method of Viterbo, which avoids…
This is an introductory survey written in Japanese on classical integrability from the viewpoint of symmetry reduction of 4-dimensional anti-self-dual Yang-Mills equations. Twistor construction methods are discussed in detail in…