Wonder Club world wonders pyramid logo
×

Lectures on Fuzzy and Fuzzy Susy Physics Book

Lectures on Fuzzy and Fuzzy Susy Physics
Lectures on Fuzzy and Fuzzy Susy Physics, Noncommutative geometry provides a powerful tool for regularizing quantum field theories in the form of fuzzy physics. Fuzzy physics maintains symmetries, has no fermion-doubling problem and represents topological features efficiently. These lecture notes, Lectures on Fuzzy and Fuzzy Susy Physics has a rating of 3.5 stars
   2 Ratings
X
Lectures on Fuzzy and Fuzzy Susy Physics, Noncommutative geometry provides a powerful tool for regularizing quantum field theories in the form of fuzzy physics. Fuzzy physics maintains symmetries, has no fermion-doubling problem and represents topological features efficiently. These lecture notes, Lectures on Fuzzy and Fuzzy Susy Physics
3.5 out of 5 stars based on 2 reviews
5
0 %
4
50 %
3
50 %
2
0 %
1
0 %
Digital Copy
PDF format
1 available   for $99.99
Original Magazine
Physical Format

Sold Out

  • Lectures on Fuzzy and Fuzzy Susy Physics
  • Written by author A. P. Balachandran
  • Published by World Scientific Publishing Company, Incorporated, April 2007
  • Noncommutative geometry provides a powerful tool for regularizing quantum field theories in the form of fuzzy physics. Fuzzy physics maintains symmetries, has no fermion-doubling problem and represents topological features efficiently. These lecture notes
  • Noncommutative geometry provides a powerful tool for regularizing quantum field theories in the form of fuzzy physics. Fuzzy physics maintains symmetries, has no fermion-doubling problem and represents topological features efficiently. These lecture notes
Buy Digital  USD$99.99

WonderClub View Cart Button

WonderClub Add to Inventory Button
WonderClub Add to Wishlist Button
WonderClub Add to Collection Button

Book Categories

Authors

Preface     vii
Introduction     1
Fuzzy Spaces     5
Fuzzy C[superscript 2]     5
Fuzzy S[superscript 3] and Fuzzy S[superscript 2]     5
The Fuzzy Sphere S[Characters not reproducible]     5
Observables of S[Characters not reproducible]     8
Diagonalizing L[superscript 2]     9
Scalar Fields on S[Characters not reproducible]     9
The Holstein-Primakoff Construction     10
CP[superscript N] and Fuzzy CP[superscript N]     11
The CP[superscript N] Holstein-Primakoff Construction     14
Star Products     17
Introduction     17
Properties of Coherent States     19
The Coherent State or Voros *-Product on the Moyal Plane     20
The Moyal *-Product on the Groenewold-Moyal Plane     23
The Weyl Map and the Weyl Symbol     23
Properties of *-Products     24
Cyclic Invariance     24
A Special Identity for the Weyl Star     25
Equivalence of *c and *w     25
Integration and Tracial States     26
The [Theta]-Expansion     27
The *-Products for the Fuzzy Sphere     28
The Coherent State *-Product *c     28
The Weyl *-Product *w     31
Scalar Fields on the Fuzzy Sphere     35
Loop Expansion     37
The One-Loop Two-Point Function     39
Numerical Simulations     43
Scalar Field Theory on Fuzzy S[superscript 2]     45
Gauge Theory on Fuzzy S[superscript 2] x S[superscript 2]     46
Instantons, Monopoles and Projective Modules     47
Free Modules, Projective Modules     47
Projective Modules on A = C[Infinity] (S2)     49
Equivalence of Projective Modules     51
Projective Modules on the Fuzzy Sphere     54
Fuzzy Monopoles and Projectors P[Characters not reproducible]     54
The Fuzzy Module for the Tangent Bundle and the Fuzzy Complex Structure     56
Fuzzy Nonlinear Sigma Models     59
Introduction     59
CP[superscript 1] Models and Projectors     60
An Action     63
CP[superscript 1]-Models and Partial Isometries     65
Relation Between P([superscript [Kappa]]) and P[subscript [Kappa]]     68
Fuzzy CP[superscript 1]-Models     69
The Fuzzy Projectors for [Kappa] > 0     69
The Fuzzy Projectors for [Kappa] < 0     70
The Fuzzy Winding Number     71
The Generalized Fuzzy Projector: Duality or BPS States     71
The Fuzzy Bound     71
CP[superscript N]-Models     73
Fuzzy Gauge Theories     77
Limits on Gauge Groups     78
Limits on Representations of Gauge Groups     79
Connection and Curvature     80
Instanton Sectors     81
The Partition Function and the [Theta]-parameter     82
The Dirac Operator and Axial Anomaly     85
Introduction     85
A Review of the Ginsparg-Wilson Algebra     85
Fuzzy Models     88
Review of the Basic Fuzzy Sphere Algebra     88
The Fuzzy Dirac Operator (No Instantons or Gauge Fields)     89
The Fuzzy Gauged Dirac Operator (No Instanton Fields)     91
The Basic Instanton Coupling     93
Mixing of Spin and Isospin     94
The Spectrum of the Dirac operator     94
Gauging the Dirac Operator in Instanton Sectors     95
Further Remarks on the Axial Anomaly     96
Fuzzy Supersymmetry     99
osp(2, 1) and osp(2, 2) Superalgebras and their Representations     100
Passage to Supergroups     106
On the Superspaces      107
The Superspace C[superscript 2, 1] and the Noncommutative C[Characters not reproducible]     107
The Supersphere S[superscript (3, 2)] and the Noncommutative S[superscript (3, 2)]     108
The Commutative Supersphere S[superscript (2, 2)]     108
The Fuzzy Supersphere S[Characters not reproducible]     112
More on Coherent States     114
The Action on the Supersphere S[superscript (2, 2)]     116
The Action on the Fuzzy Supersphere S[Characters not reproducible]     119
The Integral and Supertrace     119
OSp(2, 1) IRR's with Cut-Off N     121
The Highest Weight States and the osp(2, 2)-Invariant Action     121
The Spectrum of V     122
The Fuzzy SUSY Action     124
The *-Products     125
The *-Product on S[Characters not reproducible]     125
The *-Product on Fuzzy "Sections of Bundles"     127
More on the Properties of K[subscript ab]     129
The O(3) Nonlinear Sigma Model on S[superscript (2, 2)]     131
The Model on S[superscript (2, 2)]     131
The Model on S[Characters not reproducible]     132
Supersymmetric Extensions of Bott Projectors     133
The SUSY Action Revisited     134
Fuzzy Projectors and Sigma Models     135
SUSY Anomalies on the Fuzzy Supersphere     137
Overview     137
The Fuzzy Sphere     137
SUSY     138
Irreducible Representations     139
Casimir Operators     140
Tensor Products     141
The Supertrace and the Grade Adjoint     141
The Free Action     141
SUSY Chirality     143
Eigenvalues of V[subscript 0]     144
Fuzzy SUSY Instantons     145
Fuzzy SUSY Zero Modes and their Index Theory     146
Spectrum of K[subscript 2]     147
Index Theory and Zero Modes     149
Final Remarks     149
Fuzzy Spaces as Hopf Algebras     151
Overview     151
Basics     153
The Group and the Convolution Algebras     154
A Prelude to Hopf Algebras     155
The *-Homomorphism G* [right arrow] S[Characters not reproducible]     159
Hopf Algebra for the Fuzzy Spaces     161
Interpretation     165
The Presnajder Map     166
Bibliography     169
Index     179


Login

  |  

Complaints

  |  

Blog

  |  

Games

  |  

Digital Media

  |  

Souls

  |  

Obituary

  |  

Contact Us

  |  

FAQ

CAN'T FIND WHAT YOU'RE LOOKING FOR? CLICK HERE!!!

X
WonderClub Home

This item is in your Wish List

Lectures on Fuzzy and Fuzzy Susy Physics, Noncommutative geometry provides a powerful tool for regularizing quantum field theories in the form of fuzzy physics. Fuzzy physics maintains symmetries, has no fermion-doubling problem and represents topological features efficiently. These lecture notes, Lectures on Fuzzy and Fuzzy Susy Physics

X
WonderClub Home

This item is in your Collection

Lectures on Fuzzy and Fuzzy Susy Physics, Noncommutative geometry provides a powerful tool for regularizing quantum field theories in the form of fuzzy physics. Fuzzy physics maintains symmetries, has no fermion-doubling problem and represents topological features efficiently. These lecture notes, Lectures on Fuzzy and Fuzzy Susy Physics

Lectures on Fuzzy and Fuzzy Susy Physics

X
WonderClub Home

This Item is in Your Inventory

Lectures on Fuzzy and Fuzzy Susy Physics, Noncommutative geometry provides a powerful tool for regularizing quantum field theories in the form of fuzzy physics. Fuzzy physics maintains symmetries, has no fermion-doubling problem and represents topological features efficiently. These lecture notes, Lectures on Fuzzy and Fuzzy Susy Physics

Lectures on Fuzzy and Fuzzy Susy Physics

WonderClub Home

You must be logged in to review the products

E-mail address:

Password: