The Experts below are selected from a list of 175704 Experts worldwide ranked by ideXlab platform
Alejandro Corichi  One of the best experts on this subject based on the ideXlab platform.

polymer Quantum Mechanics and its continuum limit
Physical Review D, 2007CoAuthors: Alejandro Corichi, Tatjana Vukasinac, Jose A ZapataAbstract:A rather nonstandard Quantum representation of the canonical commutation relations of Quantum Mechanics systems, known as the polymer representation, has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop Quantum gravity known as loop Quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer Quantum Mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger Quantum Mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle, and a simple cosmological model.

hamiltonian and physical hilbert space in polymer Quantum Mechanics
Classical and Quantum Gravity, 2007CoAuthors: Alejandro Corichi, Tatjana Vukasinac, Jose A ZapataAbstract:In this paper, a version of polymer Quantum Mechanics, which is inspired by loop Quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested Schrodinger Quantum Mechanics. The kinematical cornerstone of our framework is the socalled polymer representation of the Heisenberg–Weyl (HW) algebra, which is the starting point of the construction. The dynamics is constructed as a continuum limit of effective theories characterized by a scale, and requires a renormalization of the inner product. The result is a physical Hilbert space in which the continuum Hamiltonian can be represented and that is unitarily equivalent to the Schrodinger representation of Quantum Mechanics. As a concrete implementation of our formalism, the simple harmonic oscillator is fully developed.
Jose A Zapata  One of the best experts on this subject based on the ideXlab platform.

polymer Quantum Mechanics and its continuum limit
Physical Review D, 2007CoAuthors: Alejandro Corichi, Tatjana Vukasinac, Jose A ZapataAbstract:A rather nonstandard Quantum representation of the canonical commutation relations of Quantum Mechanics systems, known as the polymer representation, has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop Quantum gravity known as loop Quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer Quantum Mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger Quantum Mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle, and a simple cosmological model.

hamiltonian and physical hilbert space in polymer Quantum Mechanics
Classical and Quantum Gravity, 2007CoAuthors: Alejandro Corichi, Tatjana Vukasinac, Jose A ZapataAbstract:In this paper, a version of polymer Quantum Mechanics, which is inspired by loop Quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested Schrodinger Quantum Mechanics. The kinematical cornerstone of our framework is the socalled polymer representation of the Heisenberg–Weyl (HW) algebra, which is the starting point of the construction. The dynamics is constructed as a continuum limit of effective theories characterized by a scale, and requires a renormalization of the inner product. The result is a physical Hilbert space in which the continuum Hamiltonian can be represented and that is unitarily equivalent to the Schrodinger representation of Quantum Mechanics. As a concrete implementation of our formalism, the simple harmonic oscillator is fully developed.
Harsh Mathur  One of the best experts on this subject based on the ideXlab platform.

relativistic non hermitian Quantum Mechanics
Physical Review D, 2014CoAuthors: Katherine Jonessmith, Harsh MathurAbstract:We develop relativistic wave equations in the framework of the new nonhermitian ${\cal PT}$ Quantum Mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of ${\cal PT}$symmetric Quantum Mechanics, and relativistic invariance. However, relaxing the constraint that in particular the mass matrix be Hermitian also allows for models that have no counterpart in conventional Quantum Mechanics. For example it is wellknown that a quartet of Weyl spinors coupled by a Hermitian mass matrix reduces to two independent Dirac fermions; here we show that the same quartet of Weyl spinors, when coupled by a nonHermitian but $\cal{PT}$ symmetric mass matrix, describes a single relativistic particle that can have massless dispersion relation even though the mass matrix is nonzero.The ${\cal PT}$generalized Dirac equation is also Lorentz invariant, unitary in time, and CPT respecting, even though as a noninteracting theory it violates ${\cal P}$ and ${\cal T}$ individually. The relativistic wave equations are reformulated as canonical fermionic field theories to facilitate the study of interactions, and are shown to maintain many of the canonical structures from Hermitian field theory, but with new and interesting new possibilities permitted by the nonhermiticity parameter $m_2$.
Jorrit Kruthoff  One of the best experts on this subject based on the ideXlab platform.

bootstrapping matrix Quantum Mechanics
Physical Review Letters, 2020CoAuthors: Xizhi Han, Sean A Hartnoll, Jorrit KruthoffAbstract:Large N matrix Quantum Mechanics is central to holographic duality but not solvable in the most interesting cases. We show that the spectrum and simple expectation values in these theories can be obtained numerically via a "bootstrap" methodology. In this approach, operator expectation values are related by symmetriessuch as time translation and SU(N) gauge invarianceand then bounded with certain positivity constraints. We first demonstrate how this method efficiently solves the conventional Quantum anharmonic oscillator. We then reproduce the known solution of large N single matrix Quantum Mechanics. Finally, we present new results on the ground state of large N two matrix Quantum Mechanics.
Tatjana Vukasinac  One of the best experts on this subject based on the ideXlab platform.

polymer Quantum Mechanics and its continuum limit
Physical Review D, 2007CoAuthors: Alejandro Corichi, Tatjana Vukasinac, Jose A ZapataAbstract:A rather nonstandard Quantum representation of the canonical commutation relations of Quantum Mechanics systems, known as the polymer representation, has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop Quantum gravity known as loop Quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer Quantum Mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger Quantum Mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle, and a simple cosmological model.

hamiltonian and physical hilbert space in polymer Quantum Mechanics
Classical and Quantum Gravity, 2007CoAuthors: Alejandro Corichi, Tatjana Vukasinac, Jose A ZapataAbstract:In this paper, a version of polymer Quantum Mechanics, which is inspired by loop Quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested Schrodinger Quantum Mechanics. The kinematical cornerstone of our framework is the socalled polymer representation of the Heisenberg–Weyl (HW) algebra, which is the starting point of the construction. The dynamics is constructed as a continuum limit of effective theories characterized by a scale, and requires a renormalization of the inner product. The result is a physical Hilbert space in which the continuum Hamiltonian can be represented and that is unitarily equivalent to the Schrodinger representation of Quantum Mechanics. As a concrete implementation of our formalism, the simple harmonic oscillator is fully developed.