Elementary derivation of the chiral anomaly

Langmann, Edwin; Mickelsson, Jouko

doi:10.1007/bf00403250

Cited by 14 publications

(13 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We will show that as both, or just one, of the two periods goes to infinity, we recover the potentials of type I, II and III, respectively. This fact was mentioned, but not proved, in [9], and a proof for the III type potential was briefly indicated in Appendix A of [91]. Set Let w km = 2πk + iβm denote the position of the double poles of V (z).…”

Section: Triplicity Of the Weierstrass Potentialmentioning

confidence: 99%

Random matrix theory and symmetric spaces

Caselle

Magnea

2004

Physics Reports

View full text Add to dashboard Cite

In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing the ensembles are in strict correspondence with symmetric spaces and the intrinsic characteristics of their restricted root lattices. Several important results can be obtained from this identification. In particular the Cartan classification of triplets of symmetric spaces with positive, zero and negative curvature gives rise to a new classification of random matrix ensembles. The review is organized into two main parts. In Part I the theory of symmetric spaces is reviewed with particular emphasis on the ideas relevant for appreciating the correspondence with random matrix theories. In Part II we discuss various applications of symmetric spaces to random matrix theories and in particular the new classification of disordered systems derived from the classification of symmetric spaces. We also review how the mapping from integrable Calogero--Sutherland models to symmetric spaces can be used in the theory of random matrices, with particular consequences for quantum transport problems. We conclude indicating some interesting new directions of research based on these identifications.Comment: 161 pages, LaTeX, no figures. Revised version with major additions in the second part of the review. Version accepted for publication on Physics Report

show abstract

Section: Triplicity Of the Weierstrass Potentialmentioning

confidence: 99%

Random matrix theory and symmetric spaces

Caselle

Magnea

2004

Physics Reports

View full text Add to dashboard Cite

show abstract

“…We now define the conditional trace Tr ǫ of an operator to be the sum of the traces of its diagonal submatrices: Tr ǫ X = 1 2 Tr[X + ǫXǫ]. (Such conditional traces have been used recently to study anomalies [28].) This conditional trace exists for Mu and we define…”

Section: The Disc and The Grassmannianmentioning

confidence: 99%

Geometric Quantization and Two Dimensional QCD

Rajeev¹,

Turgut²

1998

Communications in Mathematical Physics

View full text Add to dashboard Cite

In this article, we will discuss geometric quantization of 2d QCD with fermionic and bosonic matter fields. We identify the respective large-N c phase spaces as the infinite dimensional Grassmannian and the infinite dimensional Disc. The Hamiltonians are quadratic functions, and the resulting equations of motion for these classical systems are nonlinear. In [33], it was shown that the linearization of the equations of motion for the Grassmannian gave the 't Hooft equation. We will see that the linearization in the bosonic case leads to the scalar analog of the 't Hooft equation found in [36].

show abstract

“…It also provides an explanation how anomalies with their rich differential geometric structure can arise from explicit field theory calculations. The latter are done by calculating Feynman diagrams (see [J] and references therein) which can be interpreted as (regularized) traces of certain Hilbert space operators [LM2]; our result shows how the differential geometric structure of anomalies can be present already on the level of Hilbert space operators. We feel that this adds strong support to the expectation that NCG is relevant for quantum gauge theories.…”

Section: Introductionmentioning

confidence: 90%

Descent equations of Yang-Mills anomalies in noncommutative geometry

Langmann

1997

Journal of Geometry and Physics

Self Cite

View full text Add to dashboard Cite

Consistent Yang-Mills anomalies ω k−1 2n−k (n ∈ N, k = 1, 2, . . . , 2n) as described collectively by Zumino's descent equations δω k−1 2n−k + dω k 2n−k−1 = 0 starting with the Chern character Ch 2n = dω 0 2n−1 of a principal SU(N ) bundle over a 2n dimensional manifold are considered (i.e. ω k−1 2n−k are the ChernSimons terms (k = 1), axial anomalies (k = 2), Schwinger terms (k = 3) etc. in (2n − k) dimensions). A generalization in the spirit of Connes' noncommutative geometry using a minimum of data is found. For an arbitrary graded differential algebra Ω = ∞ k=0 Ω (k) with exterior differentiation d, form valued functions Ch 2n

show abstract

Elementary derivation of the chiral anomaly

Cited by 14 publications

References 4 publications

Random matrix theory and symmetric spaces

Random matrix theory and symmetric spaces

Geometric Quantization and Two Dimensional QCD

Descent equations of Yang-Mills anomalies in noncommutative geometry

Contact Info

Product

Resources

About