scholarly journals Path integral evaluation of the one-loop effective potential in field theory of diffusion-limited reactions

2007 ◽  
Vol 378 (2) ◽  
pp. 238-254 ◽  
Author(s):  
D. Hochberg ◽  
M.-P. Zorzano
Keyword(s):  
Field Theory ◽  
Path Integral ◽  
Effective Potential ◽  
Integral Evaluation ◽  
Diffusion Limited ◽  
The One

scholarly journals AN ALGORITHMIC APPROACH TO QUANTUM FIELD THEORY

2006 ◽  
Vol 21 (03) ◽  
pp. 405-447 ◽  
Author(s):  
MASSIMO DI PIERRO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Path Integral ◽  
Gauge Theories ◽  
Quantum Field ◽  
Algorithmic Approach ◽  
Main Emphasis ◽  
Lattice Computation ◽  
Theoretical Foundations ◽  
Minimal Residual

The lattice formulation provides a way to regularize, define and compute the Path Integral in a Quantum Field Theory. In this paper, we review the theoretical foundations and the most basic algorithms required to implement a typical lattice computation, including the Metropolis, the Gibbs sampling, the Minimal Residual, and the Stabilized Biconjugate inverters. The main emphasis is on gauge theories with fermions such as QCD. We also provide examples of typical results from lattice QCD computations for quantities of phenomenological interest.

Ring-diagram summations in the finite-temperature effective potential

1993 ◽  
Vol 71 (5-6) ◽  
pp. 227-236 ◽  
Author(s):  
M. E. Carrington
Keyword(s):  
Phase Transition ◽  
Standard Model ◽  
Effective Potential ◽  
Finite Temperature ◽  
Electroweak Phase Transition ◽  
First Order ◽  
Ring Diagram ◽  
First Order Phase Transition ◽  
The Standard Model ◽  
The One

There has been much recent interest in the finite-temperature effective potential of the standard model in the context of the electroweak phase transition. We review the calculation of the effective potential with particular emphasis on the validity of the expansions that are used. The presence of a term that is cubic in the Higgs condensate in the one-loop effective potential appears to indicate a first-order electroweak phase transition. However, in the high-temperature regime, the infrared singularities inherent in massless models produce cubic terms that are of the same order in the coupling. In this paper, we discuss the inclusion of an infinite set of these terms via the ring-diagram summation, and show that the standard model has a first-order phase transition in the weak coupling expansion.

TETRAHEDRA AND POLYNOMIAL EQUATIONS IN TOPOLOGICAL FIELD THEORY

1991 ◽  
Vol 06 (20) ◽  
pp. 3571-3598 ◽  
Author(s):  
NOUREDDINE CHAIR ◽  
CHUAN-JIE ZHU
Keyword(s):  
Field Theory ◽  
Topological Field Theory ◽  
Fundamental Representation ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Witten Theory ◽  
Topological Field ◽  
General Program ◽  
The One ◽  
Chern Simons

Some tetrahedra in SUk(2) Chern-Simons-Witten theory are computed. The results can be used to compute an arbitrary tetrahedron inductively by fusing with the fundamental representation. The results obtained are in agreement with those of quantum groups. By associating a (finite) topological field theory (FTFT) to every rational conformal field theory (RCFT), we show that the pentagon and hexagon equations in RCFT follow directly from some skein relations in FTFT. By generalizing the operation of surgery on links in FTFT, we also derive an explicit expression for the modular transformation matrix S(k) of the one-point conformal blocks on a torus in RCFT and the equations satisfied by S(k), in agreement with those required in RCFT. The implication of our results on the general program of classifying RCFT is also discussed.

Emerson's Atom and the Matter of Suffering

2009 ◽  
Vol 64 (1) ◽  
pp. 16-47
Author(s):  
Mark Noble
Keyword(s):  
Field Theory ◽  
Natural History ◽  
Classical Field Theory ◽  
Classical Field ◽  
The Other ◽  
History Of ◽  
The One ◽  
The Individual ◽  
Solid Bodies ◽  
Lines Of Force

This essay argues that Ralph Waldo Emerson's interest in the cutting-edge science of his generation helps to shape his understanding of persons as fluid expressions of power rather than solid bodies. In his 1872 "Natural History of Intellect," Emerson correlates the constitution of the individual mind with the tenets of Michael Faraday's classical field theory. For Faraday, experimenting with electromagnetism reveals that the atom is a node or point on a network, and that all matter is really the arrangement of energetic lines of force. This atomic model offers Emerson a technology for envisioning a materialized subjectivity that both unravels personal identity and grants access to impersonal power. On the one hand, adopting Faraday's field theory resonates with many of the affirmative philosophical and ethical claims central to Emerson's early essays. On the other hand, however, distributing the properties of Faraday's atoms onto the properties of the person also entails moments in which materialized subjects encounter their own partiality, limitation, and suffering. I suggest that Emerson represents these aspects of experience in terms that are deliberately discrepant from his conception of universal power. He presumes that if every experience boils down to the same lines of force, then the particular can be trivialized with respect to the general. As a consequence, Emerson must insulate his philosophical assertions from contamination by our most poignant experiences of limitation. The essay concludes by distinguishing Emersonian "Necessity" from Friedrich Nietzsche's similar conception of amor fati, which routes the affirmation of fate directly through suffering.

Diffusion-Limited Cell Dehydration: Analytical and Numerical Solutions for a Planar Model

1999 ◽  
Author(s):  
Alexander V. Kasharin ◽  
Jens O. M. Karlsson
Keyword(s):  
Analytical Solution ◽  
Numerical Solutions ◽  
Planar System ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Constant Diffusivity ◽  
A Cell ◽  
Cell Dehydration ◽  
The One

Abstract The process of diffusion-limited cell dehydration is modeled for a planar system by writing the one-dimensional diffusion-equation for a cell with moving, semipermeable boundaries. For the simplifying case of isothermal dehydration with constant diffusivity, an approximate analytical solution is obtained by linearizing the governing partial differential equations. The general problem must be solved numerically. The Forward Time Center Space (FTCS) and Crank-Nicholson differencing schemes are implemented, and evaluated by comparison with the analytical solution. Putative stability criteria for the two algorithms are proposed based on numerical experiments, and the Crank-Nicholson method is shown to be accurate for a mesh with as few as six nodes.

A NONPERTURBATIVE CALCULATION FOR THE EFFECTIVE POTENTIAL OF THE $\left(\frac{g}{4}\phi^{4}-J\phi\right)_{1+1}$ SCALAR FIELD THEORY USING THE OSCILLATOR REPRESENTATION METHOD WITH BOREL RESUMMATION

2007 ◽  
Vol 22 (06) ◽  
pp. 1265-1278
Author(s):  
ABOUZEID M. SHALABY ◽  
S. T. EL-BASYOUNY
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Phase Transition ◽  
Scalar Field ◽  
External Magnetic Field ◽  
Effective Potential ◽  
Oscillator Representation ◽  
Constructive Field Theory ◽  
Representation Method ◽  
Oscillator Representation Method

We established a resummed formula for the effective potential of [Formula: see text] scalar field theory that can mimic the true effective potential not only at the critical region but also at any point in the coupling space. We first extend the effective potential from the oscillator representation method, perturbatively, up to g3 order. We supplement perturbations by the use of a resummation algorithm, originally due to Kleinert, Thoms and Janke, which has the privilege of using the strong coupling as well as the large coupling behaviors rather than the conventional resummation techniques which use only the large order behavior. Accordingly, although the perturbation series available is up to g3 order, we found a good agreement between our resummed effective potential and the well-known features from constructive field theory. The resummed effective potential agrees well with the constructive field theory results concerning existing and order of phase transition in the absence of an external magnetic field. In the presence of the external magnetic field, as in magnetic systems, the effective potential shows nonexistence of phase transition and gives the behavior of the vacuum condensate as a monotonic increasing function of J, in complete agreement with constructive field theory methods.

scholarly journals ON THE QUANTUM THEORY OF MASSLESS SPIN-3/2 FIELD IN MINKOWSKI SPACETIME

2006 ◽  
Vol 03 (07) ◽  
pp. 1303-1312 ◽  
Author(s):  
WEIGANG QIU ◽  
FEI SUN ◽  
HONGBAO ZHANG
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Casimir Effect ◽  
Minkowski Spacetime ◽  
Quantum Field ◽  
Explicit Result ◽  
Massless Spin ◽  
The Many ◽  
The One

From the modern viewpoint and by the geometric method, this paper provides a concise foundation for the quantum theory of massless spin-3/2 field in Minkowski spacetime, which includes both the one-particle's quantum mechanics and the many-particle's quantum field theory. The explicit result presented here is useful for the investigation of spin-3/2 field in various circumstances such as supergravity, twistor programme, Casimir effect, and quantum inequality.

Sign in / Sign up

Export Citation Format

Share Document