The Yang-Mills Vacuum Wave Functional in 2+1 Dimensions

Abstract

We investigate Yang-Mills theory in 2+1 dimensions in the Schroedinger representation. The Schroedinger picture is interesting because it is well suited to explore properties of the vacuum state in the non-perturbative regime. Yet, not much analytical work has been done on this subject, and even the topic of perturbation theory in the Schroedinger representation is not well developed, especially in the case of gauge theories. In a paper by Hatfield [Phys.Lett.B 147, 435 (1984)] the vacuum wave functional for SU(2) theory was computed to O(e). In the non-perturbative regime, the most sophisticated analytical approach has been developed by Karabali et al. in a series of papers (see [Nucl.Phys.B 824, 387 (2010)] and references therein). This thesis aims to put perturbation theory in the Schroedinger representation on more solid ground by computing the vacuum wave functional for a general gauge group SU$(N_c)$ up to O$(e^2)$, utilizing modifications of these two methods. This is important since it provides us with a tool for testing non-perturbative approaches, which should reproduce the perturbative result in an appropriate limit. Furthermore, regularization and renormalization are also not well understood in the Schroedinger picture. The regularization method proposed by Karabali et al. leads to conflicting results when applied to the computation of the vacuum wave functional with the two different methods mentioned above. We aim to clarify how regularization should be implemented and develop a new regularization approach, which brings these two expressions into agreement, providing a strong check of the regularization employed. We argue that this regularization procedure is not specific to the cases studied here. It should be applied in the same way to any quantum field theory in any dimension in the Schroedinger picture.

arXiv commentPhD thesis, 229 pages, added a reference

References in corpus (26)

• Potential NRQCD: an effective theory for heavy quarkonium
• QCD phenomenology of static sources and gluonic excitations at short distances
• On the vacuum wavefunction and string tension of Yang-Mills theories in (2+1) dimensions
• A gauge-invariant Hamiltonian analysis for non-Abelian gauge theories in (2+1) dimensions
• A Self-consistent Inclusion of Magnetic Screening for the Quark-Gluon Plasma
• Planar Yang-Mills theory: Hamiltonian, regulators and mass gap
• Lattice QCD Calculation for the Physical Equation of State
• Magnetic Screening in the High Temperature Phase of the Standard Model
• Threshhold Singularities and the Magnetic Mass in Hot QCD
• QCD field strength correlator at the next-to-leading order
• The Hamiltonian Approach to Yang-Mills (2+1): An Expansion Scheme and Corrections to String Tension
• On One-Loop Gap Equations for the Magnetic Mass in d=3 Gauge Theory
• Dimensional Reduction and the Yang-Mills Vacuum State in 2+1 Dimensions
• Testing Proposals for the Yang-Mills Vacuum Wavefunctional by Measurement of the Vacuum
• Continuum limit of string formation in 3-d SU(2) LGT
• Yang-Mills Theory in 2+1 Dimensions: Coupling of Matter Fields and String-breaking Effects
• Supersymmetry and Mass Gap in 2+1 Dimensions: A Gauge Invariant Hamiltonian Analysis
• Static forces in d=2+1 SU(N) gauge theories
• Resummation scheme for 3d Yang-Mills and the two-loop magnetic mass for hot gauge theories
• Renormalization of Functional Schroedinger Equation by Background Field Method
• The Quantum Effective Action, Wave Functions and Yang-Mills (2+1)
• The QCD static potential in 2+1 dimensions at weak coupling
• The Yang-Mills vacuum wave functional in three dimensions at weak coupling
• On pure Yang-Mills theory in 3+1 dimensions: Hamiltonian, vacuum and gauge invariant variables
• The regularization and determination of the Yang-Mills vacuum wave functional in three dimensions at O(e^2)
• Numerical study of the Yang-Mills vacuum wavefunctional in D=3+1 dimensions