Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1995-05-23
Prog.Theor.Phys. 94 (1995) 1135-1146
Physics
High Energy Physics
High Energy Physics - Phenomenology
22 pages lateX. A better form of determinants is given in chapters 4 and 5
Scientific paper
10.1143/PTP.94.1135
The Euclidean version of the Yang-Mills theory is studied in four dimensions. The field is expressed non-linearly in terms of the basic variables. The field is developed inductively, adding one excitation at a time. A given excitation is added into the ``background field'' of the excitations already added, the background field expressed in a radially axial gauge about the point where the excitation is centered. The linearization of the resultant expression for the field is an expansion $$ A_\mu(x) \ \cong \ \sum_\alpha \; c_\alpha \; \psi_\mu^\alpha(x) $$ where $\psi^\alpha_\mu(x)$ is a divergence-free wavelet and $c_\alpha$ is the associated basic variable, a Lie Algebra element of the gauge group. One is working in a particular gauge, regularization is simply cutoff regularization realized by omitting wavelet excitations below a certain length scale. We will prove in a later paper that only the usual gauge-invariant counterterms are required to renormalize perturbation theory. Using related ideas, but essentially independent of the rest of paper, we find an expression for the determinant of a gauged boson or fermion field in a fixed ``small'' external gauge field. This determinant is expressed in terms of explicitly gauge invariant quantities, and again may be regularized by a cutoff regularization. We leave to later work relating these regularizations to the usual dimensional regularization.
Federbush Paul
No associations
LandOfFree
A New Formulation and Regularization of Gauge Theories Using a Non-Linear Wavelet Expansion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A New Formulation and Regularization of Gauge Theories Using a Non-Linear Wavelet Expansion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A New Formulation and Regularization of Gauge Theories Using a Non-Linear Wavelet Expansion will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-617274