Related papers: Unambiguous Phase Spaces for Subregions
The big phase space, the geometric setting for the study of quantum cohomology with gravitational descendents, is a complex manifold and consists of an infinite number of copies of the small phase space. The aim of this paper is to define a…
The problem of computing the integral cohomology ring of the symmetric square of a topological space has been of interest since the 1930s, but limited progress has been made on the general case until recently. In this work we offer a…
In this article we present the influence of a Hamiltonian saddle-node bifurcation on the high-dimensional phase space structures that mediate reaction dynamics. To achieve this goal, we identify the phase space invariant manifolds using…
We present a covariant decomposition of Einstein's Field Equations which is particularly suitable for perturbations of spherically symmetric -- and general locally rotationally symmetric -- spacetimes. Based upon the utility of the 1+3…
Many physically important mechanical systems may be described with a Lie group $G$ as configuration space. According to the well-known Noether's theorem, underlying symmetries of the Lie group may be used to considerably reduce the…
This paper discusses several functional analytic issues relevant for field theories in the context of the Hamiltonian formulation for a free, massless, scalar field defined on a closed interval of the real line. The fields that we use…
In the first part of this paper, we consider, in the context of an arbitrary hyperplane arrangement, the map between compactly supported cohomology to the usual cohomology of a local system. A formula (i.e., an explicit algebraic de Rham…
The hyperplane and proper time formalisms are discussed mainly for the spin-half particles in the quantum case. A connection between these covariant Hamiltonian formalisms is established. It is showed that choosing the space-like…
The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of…
We reformulate Fourier-space crystallography in the language of cohomology of groups. Once the problem is understood as a classification of linear functions on the lattice, restricted by a particular group relation, and identified by gauge…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
Hamiltonian mechanics of field theory can be formulated in a generally covariant and background independent manner over a finite dimensional extended configuration space. The physical symplectic structure of the theory can then be defined…
The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The…
Dynamical phase transitions are defined as non-analytic points of the large deviation function of current fluctuations. We show that for boundary driven systems, many dynamical phase transitions can be identified using the geometrical…
We develop integral geometry for non-compactly causal symmetric spaces. We define a complex horospherical transform and, for some cases, identify it with a Cauchy type integral.
Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved…
Conventional approaches to lattice gauge theories do not properly consider the topology of spacetime or of its fields. In this paper, we develop a formulation which tries to remedy this defect. It starts from a cubical decomposition of the…
In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum…
This work addresses the Hamiltonian dynamics of the Kepler problem in a deformed phase space, by considering the equatorial orbit. The recursion operators are constructed and used to compute the integrals of motion. The same investigation…
Energy transfer in the dark sector of the universe gives rise to new phenomena of special interest in modern cosmology. When dark energy is modeled as a phantom scalar field, interactions become crucial to avoid Big Rip singularities. In…