scholarly journals Euler-Poincaré Characteristic for the Oscillator Representation

2017 ◽  
pp. 1-22
Author(s):  
Jeffrey D. Adams ◽  
Dipendra Prasad ◽  
Gordan Savin
Keyword(s):  
Oscillator Representation

A Feeding-Entrainable Oscillator Representation of Time

2002 ◽  
Author(s):  
Matthew J. Pizzo ◽  
Jonathon D. Crystal
Keyword(s):  
Oscillator Representation ◽  
Representation Of Time

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.

True many-particle scattering in the oscillator representation

1998 ◽  
Vol 117 (2) ◽  
pp. 1291-1307 ◽  
Author(s):  
S. A. Zaitsev ◽  
Yu. F. Smirnov ◽  
A. M. Shirokov
Keyword(s):  
Particle Scattering ◽  
Oscillator Representation
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