arXiv subjects

K. Langfeld

Publications and source records attributed to K. Langfeld.

40 records · Page 3Linked to original sources

arXiv1993

Non-Trivial Phase Structure of $ϕ^{4}$-Theory at Finite Temperature

The effective potential for the local composite operator $ϕ^{2}(x)$ in $λϕ^{4}$-theory is investigated at finite temperature in an approach based on path-integral linearisation of the $ϕ^4 $-interaction. At zero temperature, the perturbative vacuum is unstable, because a non-trivial phase with a scalar condensate $\langle ϕ^{2} \rangle _{0}$ has lower effective action. Due to field renormalisation, $\langle λϕ^{2} \rangle _{0}$ is renormalisation group invariant and leads to the correct scale anomaly. At a critical temperature $T_{c}$ the non-perturbative phase becomes meta-stable implying a first order phase-transition to the perturbative phase. The ratio $\langleλϕ^{2} \rangle _{0} / T_{c}^{2} \approx 62$ turns out to be a universal constant.

hep-ph↗

arXiv1993

The Non-Trivial Phase of $\PHI ^4$-Theory in a Renormalisation Group Invariant Approach

Massless $ϕ^{4}$-theory is investigated in zero and four space-time dimensions. Path-integral linearisation of the $ϕ^{4}$-interaction defines an effective theory, which is investigated in a loop-expansion around the mean field. In zero dimensions this expansion converges rapidly to the exact potential obtained numerically. In four dimensions its lowest order (mean-field approximation) produces a real and convex effective potential. Two phases are found. In one the renormalisation group improved one-loop effective potential is recovered as the leading contribution near the classical minimum. This phase, however, is unstable. The second (precarious) phase is found to have lower vacuum energy density. In this phase a dynamical mass is generated. The results are renormalisation group invariant.

hep-ph↗

arXiv1993

Instanton Condensation in Field Strength Formulated QCD

Field strength formulated Yang-Mills theory is confronted with the traditional formulation in terms of gauge fields. It is shown that both formulations yield the same semiclassics, in particular the same instanton physics. However, at the tree level the field strength approach is superior because it already includes a good deal of of quantum fluctuations of the standard formulation. These quantum fluctuations break the scale invariance of classical QCD and give rise to an instanton interaction and this causes the instantons to condense and form a homogeneous instanton solid. Such the instanton solids show up in the field strength approach as homogeneous (constant up to gauge transformations) vacuum solutions. A new class of SU(N) instantons is presented which are not embeddings of SU(N-1) instantons but have non-trivial SU(N) color structure and carry winding number $n=N(N^{2}-1)/6$. These instantons generate (after condensation) the lowest action solutions of the field strength approach. The statistical weight (entropy) of different homogeneous solutions for SU(3) is numerically estimated by Parisi's stochastic quantization method. Finally, we compare instanton induced quark condensation with the condensation of quarks in the homogeneous field strength solutions. Our investigations show that the homogeneous vacuum of the field strength approach simulates in an efficient way a condensate of instantons.

hep-ph↗

arXiv1993

Instantons in Field Strength Formulated Yang-Mills Theories

It is shown that the field strength formulated Yang-Mills theory yields the same semiclassics as the standard formulation in terms of the gauge potential. This concerns the classical instanton solutions as well as the quantum fluctuations around the instanton.

hep-ph↗