Wilsonian approximated renormalization group for matrix and vector models in 2 &lt; d &lt; 4

Nishigaki, Shinsuke M.

doi:10.1016/0370-2693(96)00277-8

Cited by 16 publications

(28 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Via this route, there are exact results on the phase transition in d = 1 [20] 5 that show that the transition is different from that of the Ising model, and an approximate RG treatment that has yielded exponents in 2 < d < 4 as well [21,22]. There does not appear to be a treatment of the broken symmetry phase in this formulation of the problem-at issue is how the Ising symmetry of the planar theory large negative m 2 .…”

Section: = ∞mentioning

confidence: 99%

Phase structure of non-commutative scalar field theories

2001

View full text Add to dashboard Cite

We investigate the phase structure of non-commutative scalar field theories and find evidence for ordered phases which break translation invariance. A self-consistent oneloop analysis indicates that the transition into these ordered phases is first order. The phase structure and the existence of scaling limits provides an alternative to the structure of counter-terms in determining the renormalizability of non-commutative field theories. On the basis of the existence of a critical point in the closely related planar theory, we argue that there are renormalizable interacting non-commutative scalar field theories in dimensions two and above. We exhibit this renormalization explicitly in the large N limit of a non-commutative O(N) vector model.

show abstract

Section: = ∞mentioning

confidence: 99%

Phase structure of non-commutative scalar field theories

2001

View full text Add to dashboard Cite

show abstract

“…See [135,136] for a pedagogical introduction to the subject of the functional renormalization group. The Wilson renormalization group recursion formula was also used in [130][131][132][133][134] to study matrix scalar models which, as it turns out, are of great relevance to the limit θ −→ ∞ of noncommutative scalar field theory [137].…”

Section: Noncommutative Scalar Field Theorymentioning

confidence: 99%

Lectures on Matrix Field Theory

Ydri

2017

Lecture Notes in Physics

View full text Add to dashboard Cite

The subject of matrix field theory involves matrix models, noncommutative geometry, fuzzy physics and noncommutative field theory and their interplay. In these lectures, a lot of emphasis is placed on the matrix formulation of noncommutative and fuzzy spaces, and on the non-perturbative treatment of the corresponding field theories. In particular, the phase structure of noncommutative φ 4 theory is treated in great detail, and an introduction to noncommutative gauge theory is given.

show abstract

“…More precisely we need, as before, to expand these diagrams around k 2 = 0 but retain now the linear term in k 2 which is very difficult to do explicitly. Our estimation of the coefficient of k 2 , motivated by dimensional consideration, is obtained by the approximation of [59,60]. Explicitly we have the (3rd) rule:…”

Section: Wilson Rg Recursion Formulamentioning

confidence: 99%

“…See [63,64] for a pedagogical introduction to the subject of the functional renormalization group. The Wilson renormalization group recursion formula was also used in [58][59][60][61][62] to study matrix scalar models which, as it turns out, are of great relevance to the limit θ −→ ∞ of noncommutative scalar field theory [65].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Wilson RG of noncommutative Φ44

Ydri

Ahmim

Bouchareb

2015

Int. J. Mod. Phys. A

View full text Add to dashboard Cite

We present a study of phi-four theory on noncommutative spaces using a combination of the Wilson renormalization group recursion formula and the solution to the zero dimensional vector/matrix models at large N . Three fixed points are identified. The matrix model θ = ∞ fixed point which describes the disordered-to-non-uniform-ordered transition. The Wilson-Fisher fixed point at θ = 0 which describes the disordered-to-uniformordered transition, and a noncommutative Wilson-Fisher fixed point at a maximum value of θ which is associated with the transition between non-uniform-order and uniform-order phases. IntroductionA noncommutative field theory is a non-local field theory in which we replace the ordinary local point-wise multiplication of fields with the non-local Moyal-Weyl star product [1,2]. This product is intimately related to coherent states [6][7][8], Berezin quantization [9] and deformation quantization [10]. It is also very well understood that the underlying operator/matrix structure of the theory, exhibited by the Weyl map [5], is the singular most important difference with commutative field theory since it is at the root cause of profound physical differences between the two theories. We suggest [3] and references therein for elementary and illuminating discussion of the Moyal-Weyl product and other star products and their relations to the Weyl map and coherent states.Noncommutative field theory is believed to be of importance to physics beyond the standard model and the Hall effect [34] and also to quantum gravity and string theory [35,36]. * Email:ydri@stp.dias.ie, badis.ydri@univ-annaba.org. 1Noncommutative scalar field theories are the most simple, at least conceptually, quantum field theories on noncommutative spaces. Some of the novel quantum properties of noncommutative scalar field theory and scalar phi-four theory are as follows:

show abstract

Wilsonian approximated renormalization group for matrix and vector models in 2 < d < 4

Cited by 16 publications

References 18 publications

Phase structure of non-commutative scalar field theories

Phase structure of non-commutative scalar field theories

Lectures on Matrix Field Theory

Wilson RG of noncommutative Φ44

Contact Info

Product

Resources

About