scholarly journals Adelic Path Integrals for Quadratic Lagrangians

2003 ◽  
Vol 06 (02) ◽  
pp. 179-195 ◽  
Author(s):  
Goran S. Djordjević ◽  
Branko Dragovich ◽  
Ljubiša Nešić
Keyword(s):  
Quantum Mechanics ◽  
General Formula ◽  
Path Integral ◽  
Path Integrals ◽  
Number Fields ◽  
One Dimensional ◽  
Adelic Quantum Mechanics

Feynman's path integral in adelic quantum mechanics is considered. The propagator [Formula: see text] for one-dimensional adelic systems with quadratic Lagrangians is analytically evaluated. Obtained exact general formula has the form which is invariant under interchange of the number fields ℝ and ℚp.

scholarly journals p-Adic Path Integrals for Quadratic Actions

1997 ◽  
Vol 12 (20) ◽  
pp. 1455-1463 ◽  
Author(s):  
G. S. Djordjević ◽  
B. Dragovich
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Path Integrals ◽  
Probability Amplitude ◽  
Exact Form ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
One Dimensional ◽  
Ordinary Quantum

The Feynman path integral in p-adic quantum mechanics is considered. The probability amplitude [Formula: see text] for one-dimensional systems with quadratic actions is calculated in an exact form, which is the same as that in ordinary quantum mechanics.

Euclidean path integrals and quantum mechanics (QM)

2021 ◽  
pp. 18-41
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Correlation Functions ◽  
Path Integrals ◽  
Continuous Phase ◽  
Functional Integral ◽  
Smooth Transition ◽  
Path Integral Representation ◽  
The Matrix ◽  
Functional Measure

Functional integrals are basic tools to study first quantum mechanics (QM), and quantum field theory (QFT). The path integral formulation of QM is well suited to the study of systems with an arbitrary number of degrees of freedom. It makes a smooth transition between nonrelativistic QM and QFT possible. The Euclidean functional integral also emphasizes the deep connection between QFT and the statistical physics of systems with short-range interactions near a continuous phase transition. The path integral representation of the matrix elements of the quantum statistical operator e-β H for Hamiltonians of the simple separable form p2/2m +V(q) is derived. To the path integral corresponds a functional measure and expectation values called correlation functions, which are generalized moments, and related to quantum observables, after an analytic continuation in time. The path integral corresponding to the Euclidean action of a harmonic oscillator, to which is added a time-dependent external force, is calculated explicitly. The result is used to generate Gaussian correlation functions and also to reduce the evaluation of path integrals to perturbation theory. The path integral also provides a convenient tool to derive semi-classical approximations.

scholarly journals Path Integrals, Spontaneous Localisation, and the Classical Limit

2020 ◽  
Vol 75 (2) ◽  
pp. 131-141 ◽  
Author(s):  
Bhavya Bhatt ◽  
Manish Ram Chander ◽  
Raj Patil ◽  
Ruchira Mishra ◽  
Shlok Nahar ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Density Matrix ◽  
Path Integral ◽  
Classical Limit ◽  
Measurement Problem ◽  
Path Integrals ◽  
Path Integral Formulation ◽  
Von Neumann ◽  
Matrix Evolution ◽  
Grw Model

AbstractThe measurement problem and the absence of macroscopic superposition are two foundational problems of quantum mechanics today. One possible solution is to consider the Ghirardi–Rimini–Weber (GRW) model of spontaneous localisation. Here, we describe how spontaneous localisation modifies the path integral formulation of density matrix evolution in quantum mechanics. We provide two new pedagogical derivations of the GRW propagator. We then show how the von Neumann equation and the Liouville equation for the density matrix arise in the quantum and classical limit, respectively, from the GRW path integral.

scholarly journals ADELIC HARMONIC OSCILLATOR

1995 ◽  
Vol 10 (16) ◽  
pp. 2349-2365 ◽  
Author(s):  
BRANKO DRAGOVICH
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Functional Relation ◽  
Vacuum State ◽  
One Dimensional ◽  
High Energies ◽  
The Riemann Zeta Function ◽  
Adelic Quantum Mechanics ◽  
Riemann Zeta ◽  
Very High

Using the Weyl quantization we formulate one-dimensional adelic quantum mechanics, which unifies and treats ordinary and p-adic quantum mechanics on an equal footing. As an illustration the corresponding harmonic oscillator is considered. It is a simple, exact and instructive adelic model. Eigenstates are Schwartz-Bruhat functions. The Mellin transform of the simplest vacuum state leads to the well-known functional relation for the Riemann zeta function. Some expectation values are calculated. The existence of adelic matter at very high energies is suggested.

NELSON'S STOCHASTIC MECHANICS BY MEANS OF FEYNMAN PATH INTEGRALS

2000 ◽  
Vol 14 (03) ◽  
pp. 73-78 ◽  
Author(s):  
LUIZ C. L. BOTELHO
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Path Integrals ◽  
Order Equation ◽  
Feynman Path Integral ◽  
Stochastic Mechanics ◽  
Path Integral Formulation ◽  
Feynman Path ◽  
First Order ◽  
Feynman Path Integrals

We show that Nelson's stochastic mechanics suitably formulated as a Hamilton–Jacobi first-order equation leads straightforwardly to the Feynman path integral formulation of quantum mechanics.

QUANTUM MECHANICS AND PATH INTEGRALS IN SPACES WITH CURVATURE AND TORSION

1989 ◽  
Vol 04 (24) ◽  
pp. 2329-2337 ◽  
Author(s):  
H. KLEINERT
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Path Integral ◽  
Affine Space ◽  
Correspondence Principle ◽  
Integral Formula ◽  
Path Integrals ◽  
Physical Systems ◽  
Curvature And Torsion ◽  
Quantization Rules

We point out that there is a natural geometric procedure for constructing the quantum theory of a particle in a general metric-affine space with curvature and torsion. Quantization rules are presented and expressed in the form of a simple path integral formula which specifies compactly a new combined equivalence and correspondence principle. The associated Schrödinger equation has no extra curvature nor torsion terms that have plagued earlier attempts. Several well-known physical systems are invoked to suggest the correctness of the proposed theory.

scholarly journals The Caldirola–Kanai Theory from "Brownian" Path Integral Quantum Mechanics

1998 ◽  
Vol 12 (14n15) ◽  
pp. 569-573 ◽  
Author(s):  
Luiz C. L. Botelho ◽  
Edson P. da Silva
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
One Dimensional ◽  
Brownian Path ◽  
Integral Quantum

We deduce the classsical one-dimensional Caldirola–Kanai action from quantum mechanics, at the WKB limit, formulated as an electronic flux interacting with an environment in the Langevin–Brownian phenomenological path integral framework.

scholarly journals EXACTNESS IN THE PATH INTEGRAL OF THE COULOMB POTENTIAL IN ONE SPACE DIMENSION

2008 ◽  
Vol 23 (36) ◽  
pp. 3057-3076 ◽  
Author(s):  
SEJII SAKODA
Keyword(s):  
Path Integral ◽  
Bound States ◽  
Space Dimension ◽  
Path Integrals ◽  
Momentum Representation ◽  
Integral Theorem ◽  
One Dimensional ◽  
Scattering States ◽  
Pole Structure ◽  
Cauchy’S Integral Theorem

We solve time-sliced path integrals of one-dimensional Coulomb system in an exact manner. In formulating path integrals, we make use of the Duru–Kleinert transformation with Fujikawa's gauge theoretical technique. Feynman kernels in the momentum representation both for bound states and scattering states will be obtained with clear pole structure that explains the exactness of the path integral. The path integrals presented here can be, therefore, evaluated exactly by making use of Cauchy's integral theorem.

scholarly journals AdS2 × S2 × CY2 solutions in Type IIB with 8 supersymmetries

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yolanda Lozano ◽  
Carlos Nunez ◽  
Anayeli Ramirez
Keyword(s):  
Quantum Mechanics ◽  
Riemann Surface ◽  
Central Charge ◽  
Global Solutions ◽  
Infinite Family ◽  
Dimensional System ◽  
One Dimensional

Abstract We present a new infinite family of Type IIB supergravity solutions preserving eight supercharges. The structure of the space is AdS2 × S2 × CY2 × S1 fibered over an interval. These solutions can be related through double analytical continuations with those recently constructed in [1]. Both types of solutions are however dual to very different superconformal quantum mechanics. We show that our solutions fit locally in the class of AdS2 × S2 × CY2 solutions fibered over a 2d Riemann surface Σ constructed by Chiodaroli, Gutperle and Krym, in the absence of D3 and D7 brane sources. We compare our solutions to the global solutions constructed by Chiodaroli, D’Hoker and Gutperle for Σ an annulus. We also construct a cohomogeneity-two family of solutions using non-Abelian T-duality. Finally, we relate the holographic central charge of our one dimensional system to a combination of electric and magnetic fluxes. We propose an extremisation principle for the central charge from a functional constructed out of the RR fluxes.

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