arXiv subjects

Jose A. Magpantay

Publications and source records attributed to Jose A. Magpantay.

23 records · Page 2Linked to original sources

arXiv2003

The Geometrical Basis of the Nonlinear Gauge

We consider Yang-Mills theory in Euclidean space-time $(R^4)$ and construct its configuration space. The orbits are first shown to form a congruence set. Then we discuss the orthogonal gauge condition in Abelian theory and show that Coulomb-like surfaces foliate the entire configuration space. In the non-Abelian case, where these exists no global orthogonal gauge, we derive the non-linear gauge proposed previously by the author by modifying the orthogonality condition. However, unlike the Abelian case, the entire configuration space cannot be foliated by submanifolds defined by the non-linear gauge. The foliation is only limited to the non-perturbative regime of Yang-Mills theory.

hep-th↗

arXiv2003

Effective "Gluon" Dynamics in a Stochastic Vacuum

Using the new scalar and vector degrees of freedom derived from the non-linear gauge condition (grad-dot-D)(grad-dot-A)=0, we show that the effective dynamics of the vector fields (identified as ``gluons'') in the stochastic vacuum defined by the scalars result in the vector fields acquiring a range of possible masses and losing their self-interactions. From this range of masses, we derive the mass gap in pure Yang-Mills theory. Finally, we comment on the gauge-invariance of the result.

hep-th↗

arXiv2001

Direct Quantization of Open Dissipative Systems

Open, dissipative systems subject to a random force are directly quantized. The starting point is the effective action derived using the method of Parisi-Sourlas. Since the effective action is second-order, the method of Ostrogradsky was used to quantize the system canonically. In the case of the harmonic oscillator, the relevant Green function can be computed exactly. In the general case, a perturbation expansion, involving time-dependent (memory) terms, can be defined.

cond-mat↗

arXiv1999

The Parisi-Sourlas Mechanism in Yang-Mills Theory?

The Parisi-Sourlas mechanism is exhibited in pure Yang-Mills theory. Using the new scalar degrees of freedom derived from the non-linear gauge condition, we show that the non-perturbative sector of Yang-Mills theory is equivalent to a 4D O(1,3) sigma model in a random field. We then show that the leading term of this equivalent theory is invariant under supersymmetry transformations where (x^{2}+\thetabarθ) is unchanged. This leads to dimensional reduction proving the equivalence of the non-perturbative sector of Yang-Mills theory to a 2D O(1,3) sigma model.

hep-th↗

arXiv1999

The Confinement Mechanism in Yang-Mills Theory?

Using the recently proposed non-linear gauge condition, we show the area law behavior of the Wilson loop and the linear dependence of the instantaneous gluon propagator. The field configurations responsible for confinement are those in the non-linear sector of the gauge-fixing condition (the linear sector being the Coulomb gauge). The non-linear sector is actually composed of "Gribov horizons" on the surfaces parallel to the Coulomb surface. In this sector, the gauge field can be expressed in terms of a scalar field and a new vector field. The effective dynamics of the scalar field suggests non-perturbative effects. This was confirmed by showing that all spherically symmetric (in 4-D Euclidean) scalar fields are classical solutions and averaging these solutions using a qaussian distribution (thereby treating these fields as random) lead to confinement. In essence the confinement mechanism is not quantum mechanical in nature but simply a statistical treatment of classical spherically symmetric fields on the "horizons" of the surfaces parallel to the Coulomb surface.

hep-th↗