scholarly journals CASIMIR ENERGY OF CONFINED FIELDS: A ROLE OF THE RG-INVARIANCE

2002 ◽  
Vol 17 (06n07) ◽  
pp. 874-878 ◽  
Author(s):  
IGOR O. CHEREDNIKOV
Keyword(s):  
Renormalization Group ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Casimir Energy ◽  
Bag Model ◽  
Group Invariance ◽  
Fermion Fields ◽  
Mit Bag Model

A role of the renormalization group invariance in calculations of the ground state energy for models with confined fermion fields is discussed. The case of the (1+1)D MIT bag model with the massive fermions is studied in detail.

scholarly journals Glueball spectra from a matrix model of pure Yang–Mills theory

2018 ◽  
Vol 33 (13) ◽  
pp. 1850073 ◽  
Author(s):  
Nirmalendu Acharyya ◽  
A. P. Balachandran ◽  
Mahul Pandey ◽  
Sambuddha Sanyal ◽  
Sachindeo Vaidya
Keyword(s):  
Renormalization Group ◽  
Excellent Agreement ◽  
Matrix Model ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Yang Mills ◽  
Three Sphere ◽  
Simple Matrix

We present variational estimates for the low-lying energies of a simple matrix model that approximates SU(3) Yang–Mills theory on a three-sphere of radius R. By fixing the ground state energy, we obtain the (integrated) renormalization group (RG) equation for the Yang–Mills coupling g as a function of R. This RG equation allows to estimate the mass of other glueball states, which we find to be in excellent agreement with lattice simulations.

USING EVOLUTIONARY ALGORITHM TO CALCULATE THE GROUND-STATE ENERGY OF DOUBLE-ELECTRON ATOMS IN A UNIFORM MAGNETIC FIELD (B ≤ 109G)

2000 ◽  
Vol 11 (01) ◽  
pp. 183-194 ◽  
Author(s):  
LIANJUN LIU ◽  
LI ZHAO ◽  
YOUDONG MAO ◽  
DONG YU ◽  
JINGWEN XU ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Evolutionary Algorithm ◽  
Ground State Energy ◽  
Ground State ◽  
Uniform Magnetic Field ◽  
State Energy ◽  
Electron System ◽  
Energy Calculation ◽  
Double Electron

It is very difficult to calculate the accurate ground-state energies of the double-electron atom like helium in a uniform magnetic field. By using the modified configuration interaction (MCI) method and the evolutionary algorithm (EA), we obtained highly accurate results. We discuss the role of magnetic field in the ground state of the double-electron system and the possibility of variational ground-state energy calculation by using evolutionary algorithm directly. Results show that compared with other algorithms, such as the simplex method, EA is more efficient in calculating atomic energies, and can be used in other fields of physics.

scholarly journals HEAT KERNEL COEFFICIENTS AND DIVERGENCIES OF THE CASIMIR ENERGY FOR THE DISPERSIVE SPHERE

2002 ◽  
Vol 17 (06n07) ◽  
pp. 813-819 ◽  
Author(s):  
M. BORDAG ◽  
K. KIRSTEN
Keyword(s):  
Electromagnetic Field ◽  
Heat Kernel ◽  
Ground State Energy ◽  
Ground State ◽  
High Frequency ◽  
Vacuum Energy ◽  
State Energy ◽  
Casimir Energy ◽  
Divergent Part

The first heat kernel coefficients are calculated for a dispersive ball whose permittivity at high frequency differs from unity by inverse powers of the frequency. The corresponding divergent part of the vacuum energy of the electromagnetic field is given and ultraviolet divergencies are seen to be present. Also in a model where the number of atoms is fixed the pressure exhibits infinities. As a consequence, the ground-state energy for a dispersive dielectric ball cannot be interpreted easily.

scholarly journals ON SPECTRAL RENORMALIZATION GROUP

2009 ◽  
Vol 21 (04) ◽  
pp. 511-548 ◽  
Author(s):  
JÜRG FRÖHLICH ◽  
MARCEL GRIESEMER ◽  
ISRAEL MICHAEL SIGAL
Keyword(s):  
Renormalization Group ◽  
Ground State Energy ◽  
Ground State ◽  
Quantum Electrodynamics ◽  
Spectral Properties ◽  
State Energy ◽  
Theoretical Models ◽  
Companion Paper ◽  
Limiting Absorption Principle ◽  
Relativistic Matter

The operator-theoretic renormalization group (RG) methods are powerful analytic tools to explore spectral properties of field-theoretical models such as quantum electrodynamics (QED) with non-relativistic matter. In this paper, these methods are extended and simplified. In a companion paper, our variant of operator-theoretic RG methods is applied to establishing the limiting absorption principle in non-relativistic QED near the ground state energy.

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