Continuum version of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math>theory in light-front quantization

Grangé, P.; Ullrich, Peter; Werner, E.

doi:10.1103/physrevd.57.4981

Cited by 15 publications

(24 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In CLCQ the free field ϕ 0 (X) is an operator valued distribution [4] with a generalized Fock expansion built out of C ∞ -test functions with compact support in IR 2 . It is written as…”

Section: Haag Series Equations Of Motion 21 Haag Series In Second Omentioning

confidence: 99%

See 1 more Smart Citation

Critical properties of (1+1)-dimensionalφ4theory in light-cone quantization

Salmons¹,

Grangé²,

Werner³

2002

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

The dynamics of the phase transition of the continuum Φ 4 1+1 -theory in Light Cone Quantization is reexamined taking into account fluctuations of the order parameter < Φ > in the form of dynamical zero mode operators (DZMO) which appear in a natural way via the Haag expansion of the field Φ(x) of the interacting theory. The inclusion of the DZM-sector changes significantly the value of the critical coupling, bringing it in agreement within 2% with the most recent Monte-Carlo and high temperature/strong coupling estimates. The critical slowing down of the DZMO governs the low momentum behavior of the dispersion relation through invariance of this DZMO under conformal transformations preserving the local light cone structure. The critical exponent η characterising the scaling behaviour at k 2 → 0 comes out in agreement with the known value 0.25 of the Ising universality class. η is made of two contributions: one, analytic (75%) and another (25%) which can be evaluated only numerically with an estimated error of 3%. The β-function is then found from the non-perturbative expression of the physical mass. It is non-analytic in the coupling constant with a critical exponent ω = 2. However, at D = 2, ω is not parametrisation independent with respect to the space of coupling constants due to this strong non-analytic behaviour.

show abstract

“…In CLCQ the free field ϕ 0 (X) is an operator valued distribution [4] with a generalized Fock expansion built out of C ∞ -test functions with compact support in IR 2 . It is written as…”

Section: Haag Series Equations Of Motion 21 Haag Series In Second Omentioning

confidence: 99%

“…To lowest order in the Haag expansion the equation was just 1 − [6] this has to be translated [4] into the reduced coupling unit r which is just 1 at the perturbative one loop level. To the above values of g (0) c and g c corresponds the values r = 1.5 and r = 1.71.…”

Section: Iterative Proceduresmentioning

confidence: 99%

Critical properties of (1+1)-dimensionalφ4theory in light-cone quantization

Salmons¹,

Grangé²,

Werner³

2002

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

show abstract

“…For k + = 0 the usual zero mode component of ψ 2 is obtained [1].Ω k is diagonal in the number of particles but it can transfer momentum ±k + , though it is translationally invariant. This property is a consequence of motion in a periodic background field.…”

Section: Dynamical Zero Mode (Dzm) In ψmentioning

confidence: 99%

“…The properties of the test function f (k + ) are discussed in [1] : its effect is to render the integral finite at both ends of the spectrum in k + and the parameter entering any possible form of f (k + ) is related in an essential way to the final renormalization procedure of the theory.…”

Section: Field Decompositionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamical zero modes and criticality in continuous light-cone quantization of Φ1+14

Grangé

Salmons

Werner

2002

Nuclear Physics B - Proceedings Supplements

View full text Add to dashboard Cite

Critical behaviour of the 2D scalar field theory in the LC framework is reviewed. The notion of dynamical zero modes is introduced and shown to lead to a non trivial covariant dispersion relation only for Continuous LC Quantization (CLCQ). The critical exponent η is found to be governed by the behaviour of the infinite volume limit under conformal transformations properties preserving the local LC structure. The β-function is calculated exactly and found non-analytic, with a critical exponent ω = 2, in agreement with the conformal field theory prediction of Calabrese et al.

show abstract

Untitled

Chabysheva¹

2018

Light Cone 2016

View full text Add to dashboard Cite

There is a discrepancy between light-front and equal-time values for the critical coupling of twodimensional φ 4 theory. A proposed resolution is to take into account the difference between mass renormalizations in the two quantizations. This distinction was first discussed by M. Burkardt. It prevents direct comparison of bare parameters; however, a method proposed here allows calculation of the difference and thereby resolves the discrepancy. We also consider the consequences of allowing a sector-dependent constituent mass.a Based on a talk contributed to the Lightcone 2016 workshop, Lisbon, Portugal, September 5-8, 2016.

show abstract

Continuum version ofφ1+14theory in light-front quantization

Cited by 15 publications

References 19 publications

Critical properties of (1+1)-dimensionalφ4theory in light-cone quantization

Critical properties of (1+1)-dimensionalφ4theory in light-cone quantization

Dynamical zero modes and criticality in continuous light-cone quantization of Φ1+14

Untitled

Contact Info

Product

Resources

About