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Homological Perturbation Theory for Nonperturbative Integrals
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary...
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On Three Magnetic Relativistic Schrödinger Operators and Imaginary-Time Path Integrals
Three magnetic relativistic Schrödinger operators are considered corresponding to the classical relativistic Hamiltonian symbol with magnetic vector...
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A Survey on Mathematical Feynman Path Integrals: Construction, Asymptotics, Applications
Theory and main applications of infinite dimensional oscillatory integrals are discussed, with special attention to the mathematical realization of...
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The Ground State of Certain Coulomb Systems and Feynman-Kac Exponentials
We give a lower bound for the ground state energy of certain Coulomb Hamiltonians using the Feynman-Kac formula. We show that this bound is very...
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Stochastic Correction to the Semiclassical Evolution of Quantum Wave Packets
We represent the quantum evolution as a stochastic classical evolution. The deviation of the quantum wave packet from the classical trajectory is...
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Ground State of a Quantum Particle Coupled to a Scalar Bose Field
We use methods from functional integration to prove the existence and uniqueness of the ground state of a confined quantum particle coupled to a...
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Path Integrals for a Class of P-Adic Schrödinger Equations
The theme of doing quantum mechanics on all Abelian groups goes back to Schwinger and Weyl. If the group is a vector space of finite dimension over a...
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Spectral stochastic processes arising in quantum mechanical models with a non-L 2 ground state
A functional integral representation is given for a large class of quantum mechanical models with a non- L 2 ground state. As a prototype, the...
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Generalized measures in gauge theory
Let P → M be a principal G -bundle. We construct well-defined analogs of Lebesgue measure on the space
A of connections on P and Haar measure on the groupG ... -
The star exponential and path integrals on compact groups II: The weyl character formula
This is a continuation of the work begun by Cadavid and Nakashima in Lett. Math. Phys. 23 , 111–115 (1991). An expression for the Weyl Character...
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Ground-state density of the pauli operator in the large field limit
The ground-state density of the Pauli operator in the case of a nonconstant magnetic field with constant direction is studied. It is shown that in...
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The star exponential and path integrals on compact groups
Using the star exponential, a path integral is constructed for arbitrary compact Lie groups. This is a globalization of the results of Alcalde,...