Multigrid Monte Carlo for a bose field in an external gauge field

1990 ◽  
Vol 331 (2) ◽  
pp. 531-540 ◽  
Author(s):  
Arjan Hulsebos ◽  
Jan Smit ◽  
Jeroen C. Vink
Keyword(s):  
Monte Carlo ◽  
Gauge Field ◽  
External Gauge

scholarly journals The renormalization group and the effective action

2011 ◽  
Vol 89 (3) ◽  
pp. 277-280 ◽  
Author(s):  
D. G.C. McKeon
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Gauge Field ◽  
Effective Potential ◽  
Effective Action ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
The One ◽  
External Gauge

The renormalization group is used to sum the leading-log (LL) contributions to the effective action for a large constant external gauge field in terms of the one-loop renormalization group (RG) function β, the next-to-leading-log (NLL) contributions in terms of the two-loop RG function, etc. The log-independent pieces are not determined by the RG equation, but can be fixed by considering the anomaly in the trace of the energy-momentum tensor. Similar considerations can be applied to the effective potential V for a scalar field [Formula: see text]; here the log-independent pieces are fixed by the condition [Formula: see text].

scholarly journals THE SU(2) GLOBAL ANOMALY THROUGH LEVEL CIRCLING

1994 ◽  
Vol 09 (06) ◽  
pp. 501-514 ◽  
Author(s):  
MINOS AXENIDES ◽  
HOLGER BECH NIELSEN ◽  
ANDREI JOHANSEN
Keyword(s):  
Gauge Theory ◽  
Dirac Operator ◽  
Gauge Field ◽  
Complex Plane ◽  
Spinor Representation ◽  
Yukawa Couplings ◽  
Zero Modes ◽  
Global Anomaly ◽  
External Gauge

We discuss a novel manifestation of the SU(2) global anomaly in an SU(2) gauge theorywith an odd number of chiral quark doublets and arbitrary Yukawa couplings. We arguethat the massive four-dimensional Euclidean Dirac operator is non-Hermitian with itsspectrum of eigenvalues (λ, −λ) lying in pairs in the complex plane. Consequently theexistence of an odd number of normalizable zero modes of the four-dimensional massiveDirac operator is equivalent to a fermionic level exchange phenomenon, level “circling,”under continuous topologically non-trivial deformations of the external gauge field. Moregenerally global anomalies are a manifestation of fermionic level “circling” in any SP(2n)gauge theory with an odd number of massive fermions in the spinor representation andarbitrary Yukawa couplings.

TOPOLOGY COLLAPSE OF NONTRIVIAL U(1)-BUNDLE ON LATTICIZED SPHERE

1988 ◽  
Vol 03 (15) ◽  
pp. 1489-1497
Author(s):  
HIROSHI KOIBUCHI ◽  
MITSURU YAMADA
Keyword(s):  
Monte Carlo ◽  
Statistical Mechanics ◽  
Gauge Field ◽  
Low Temperatures ◽  
Field Configuration ◽  
Chern Number ◽  
Monte Carlo Technique ◽  
Metastable States ◽  
Two Dimensional ◽  
Gauge Model

Applying the Monte Carlo technique, we study the statistical mechanics of U(1) gauge model on two dimensional spherical lattice of the Mercator type. Special emphasis is put on the topology of the gauge-field configuration. At sufficiently low temperatures, we demonstrate the existence of many metastable states, each of which has a well-defined Chern number. At higher temperatures, we observe how they lose their topology and collapse.

scholarly journals Z2 GAUGE MATTER COUPLED TO 4-D SIMPLICIAL QUANTUM GRAVITY

1994 ◽  
Vol 09 (27) ◽  
pp. 2527-2541 ◽  
Author(s):  
J. AMBJØRN ◽  
J. JURKIEWICZ ◽  
S. BILKE ◽  
Z. BURDA ◽  
B. PETERSSON
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Quantum Gravity ◽  
Gauge Field ◽  
Critical Point ◽  
Order Phase Transition ◽  
Critical Index ◽  
Second Order Phase Transition

Employing Monte-Carlo simulation we study the phase diagram of a Z2 gauge field coupled to simplicial quantum gravity. We localize a critical point of the model where both the matter and gravity sectors have a second order phase transition. We found the value of the critical index γg=0.16(4) of the gravity susceptibility at the critical point.

Sign in / Sign up

Export Citation Format

Share Document