17,621 research outputs found
Generalized Schroedinger equation in Euclidean field theory
We investigate the idea of a "general boundary" formulation of quantum field
theory in the context of the Euclidean free scalar field. We propose a precise
definition for an evolution kernel that propagates the field through arbitrary
spacetime regions. We show that this kernel satisfies an evolution equation
which governs its dependence on deformations of the boundary surface and
generalizes the ordinary (Euclidean) Schroedinger equation. We also derive the
classical counterpart of this equation, which is a Hamilton-Jacobi equation for
general boundary surfaces.Comment: 25 pages, 11 figure
Algorithmic derivation of functional renormalization group equations and Dyson-Schwinger equations
We present the Mathematica application DoFun which allows to derive
Dyson-Schwinger equations and renormalization group flow equations for n-point
functions in a simple manner. DoFun offers several tools which considerably
simplify the derivation of these equations from a given physical action. We
discuss the application of DoFun by means of two different types of quantum
field theories, namely a bosonic O(N) theory and the Gross-Neveu model.Comment: 40 pages, 12 figs.; corresponds to published versio
Particle Propagator in Elementary Quantum Mechanics: a New Path Integral Derivation
This paper suggests a new way to compute the path integral for simple quantum
mechanical systems. The new algorithm originated from previous research in
string theory. However, its essential simplicity is best illustrated in the
case of a free non relativistic particle, discussed here, and can be
appreciated by most students taking an introductory course in Quantum
Mechanics. Indeed, the emphasis is on the role played by the {\it entire family
of classical trajectories} in terms of which the path integral is computed
exactly using a functional representation of the Dirac delta-distribution. We
argue that the new algorithm leads to a deeper insight into the connection
between classical and quantum systems, especially those encountered in high
energy physics.Comment: LaTex uses iopams package, 15pages, no figures, in print on Euro.J.of
Phy
Inequivalent Quantizations and Holonomy Factor from the Path-Integral Approach
A path-integral quantization on a homogeneous space G/H is proposed based on
the guiding principle `first lift to G and then project to G/H'. It is then
shown that this principle gives a simple procedure to obtain the inequivalent
quantizations (superselection sectors) along with the holonomy factor (induced
gauge field) found earlier by algebraic approaches. We also prove that the
resulting matrix-valued path-integral is physically equivalent to the
scalar-valued path-integral derived in the Dirac approach, and thereby present
a unified viewpoint to discuss the basic features of quantizing on
obtained in various approaches so far.Comment: 21 pages, uses Plain Te
Quantal Brownian Motion - Dephasing and Dissipation
We analyze quantal Brownian motion in dimensions using the unified model
for diffusion localization and dissipation, and Feynman-Vernon formalism. At
high temperatures the propagator possess a Markovian property and we can write
down an equivalent Master equation. Unlike the case of the
Zwanzig-Caldeira-Leggett model, genuine quantum mechanical effects manifest
themselves due to the disordered nature of the environment. Using Wigner
picture of the dynamics we distinguish between two different mechanisms for
destruction of coherence. The analysis of dephasing is extended to the low
temperature regime by using a semiclassical strategy. Various results are
derived for ballistic, chaotic, diffusive, both ergodic and non-ergodic motion.
We also analyze loss of coherence at the limit of zero temperature and clarify
the limitations of the semiclassical approach. The condition for having
coherent effect due to scattering by low-frequency fluctuations is also pointed
out. It is interesting that the dephasing rate can be either larger or smaller
than the dissipation rate, depending on the physical circumstances.Comment: LaTex, 23 pages, 4 figures, published vesio
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