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On the vacuum wavefunction and string tension of Yang-Mills theories in ( 2 + 1 ) dimensions
| Content Provider | Semantic Scholar |
|---|---|
| Copyright Year | 1998 |
| Abstract | We present an analytical continuum calculation, starting from first principles, of the vacuum wavefunction and string tension for pure Yang-Mills theories in (2+1) dimensions, extending our previous analysis using gauge-invariant matrix variables. The vacuum wavefunction is consistent with what is expected at both high and low momentum regimes. The value of the string tension is in very good agreement with recent lattice Monte Carlo evaluations. In recent papers we have done a Hamiltonian analysis of non-Abelian gauge theories in two spatial dimensions [1,2]. The analysis was facilitated by a special matrix parametrization for the gauge potentials and the use of some results from conformal field theory. We obtained results regarding the mass gap and wavefunctions as well as a reduction of the Hamiltonian to gauge-invariant degrees of freedom. In this paper, we shall extend our analysis with a more exact calculation of the vacuum wavefunction and the string tension. Our results are in very good agreement with recent Monte Carlo simulations of (2+1)-dimensional gauge theories. It should be emphasized that our work is an analytical calculation directly in the continuum and based on first principles. We shall begin by a brief recapitulation of the main results. In our previous papers, we have used the A-diagonal representation. In this paper, we give a reduction of the Hamiltonian to the gauge-invariant degrees of freedom in a representation independent way, i.e., valid for the E-representation as well as the A-representation, before specializing to the A-representation and recovering the previous result. As far as the kinetic energy operator is concerned, the vacuum wavefunction is trivially obtained. The effect of the potential energy is included in a systematic perturbation expansion. The expansion parameter is k/m, where m = e 2cA 2π is the mass parameter which emerges from our analysis and k is the characteristic momentum. From the vacuum wavefunction, with first order corrections due to the potential energy, we calculate the expectation value of the Wilson loop operator. This obeys the area law and gives the value of the string tension. By summing up sequences of terms in the 1/m-expansion, the vacuum wavefunction is reexpressed in terms of a series in J , where J is a current to be introduced below. The terms in this series interpolate smoothly between low and high momentum (standard perturbative) regimes. Similar analysis for the low energy excitation spectrum of the Hamiltonian is outlined. We consider the Hamiltonian version of an SU(N)-gauge theory in the A0 = 0 gauge. The gauge potentials are Ai = −itAi , i = 1, 2, where t are hermitian (N ×N)-matrices which form a basis of the Lie algebra of SU(N) with [t, t] = ift, Tr(tt) = 12δ . The Hamiltonian can be written as H = T + V, T = e 2 2 ∫ E i E a i , V = 1 2e2 ∫ |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/hep-th/9804132v2.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/hep-th/9804132v1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Aortic Valve Insufficiency Byers-Yang theorem Dimensions Energy operator Evaluation Excitation Expectation value (quantum mechanics) Hamiltonian (quantum mechanics) Interpolation Kinetics Leucaena pulverulenta Like button Monte Carlo method Paper Perturbation theory (quantum mechanics) Population Parameter Quantum field theory Simulation Smoothing Tension Triune continuum paradigm YANG |
| Content Type | Text |
| Resource Type | Article |
