Download ashok das quantum field theory pdf 2023

In this post can download Lectures on Quantum Field Theory by Ashok Das Book pdf for free. Ashok das quantum field theory pdf can be very helpful for a good command over quantum mechanism. This book is not only helpful for under-graduation and post-graduation but also useful in competition like IITJAM, CSIR-NET, GATE etc.

Download lectures on quantum mechanics ashok das pdf

Download ashok das quantum field theory pdf 2023
Download ashok das quantum field theory pdf 2023

The Lectures on Quantum field theory pdf author is Ashok Das who is a professor in university of Rochester, USA. Quantum Field Theory which is known to be a difficult subject but using quantum field theory pdf of ashok das make it easier. It is a good book in quantum field theory.

It is basically a compendium of classroom lecture notes. Professor Das has structured the book to enable the reader to have a bird’s eye view of the entire subject.

Chapter content of ashok das quantum mechanics pdf:

The book contain following chapters and topics.

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1 Relativistic equations . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Notations. . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Klein-Gordon equation . . . . . . . . . . . . . . . . . 10
1.3.1 Klein paradox . . . . . . . . . . . . . . . . . . . 14
1.4 Dirac equation. . . . . . . . . . . . . . . . . . . . . . 19
1.5 References . . . . . . . . . . . . . . . . . . . . . . . . 26


2 Solutions of the Dirac equation . . . . . . . . . . . . . . . . 27
2.1 Plane wave solutions . . . . . . . . . . . . . . . . . . 27
2.2 Normalization of the wave function . . . . . . . . . . 34
2.3 Spin of the Dirac particle. . . . . . . . . . . . . . . . 40
2.4 Continuity equation. . . . . . . . . . . . . . . . . . . 44
2.5 Dirac’s hole theory . . . . . . . . . . . . . . . . . . . 47
2.6 Properties of the Dirac matrices . . . . . . . . . . . . 49
2.6.1 Fierz rearrangement . . . . . . . . . . . . . . . 58
2.7 References . . . . . . . . . . . . . . . . . . . . . . . . 62


3 Properties of the Dirac equation . . . . . . . . . . . . . . . 65
3.1 Lorentz transformations . . . . . . . . . . . . . . . . 65
3.2 Covariance of the Dirac equation . . . . . . . . . . . 72
3.3 Transformation of bilinears. . . . . . . . . . . . . . . 82
3.4 Projection operators, completeness relation . . . . . 84
3.5 Helicity . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.6 Massless Dirac particle . . . . . . . . . . . . . . . . . 94
3.7 Chirality . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.8 Non-relativistic limit of the Dirac equation. . . . . . 105
3.9 Electron in an external magnetic field . . . . . . . . 107
3.10 Foldy-Wouthuysen transformation. . . . . . . . . . . 111
3.11 Zitterbewegung . . . . . . . . . . . . . . . . . . . . . 117
3.12 References . . . . . . . . . . . . . . . . . . . . . . . . 122


4 Representations of Lorentz and Poincar´e groups . . . . . . 125
4.1 Symmetry algebras . . . . . . . . . . . . . . . . . . . 125
4.1.1 Rotation . . . . . . . . . . . . . . . . . . . . . . 125
4.1.2 Translation . . . . . . . . . . . . . . . . . . . . 129
4.1.3 Lorentz transformation . . . . . . . . . . . . . 130
4.1.4 Poincar´e transformation . . . . . . . . . . . . . 133
4.2 Representations of the Lorentz group . . . . . . . . . 135
4.2.1 Similarity transformations and representations 140
4.3 Unitary representations of the Poincar´e group . . . . 147
4.3.1 Massive representation . . . . . . . . . . . . . . 151
4.3.2 Massless representation . . . . . . . . . . . . . 155
4.4 References . . . . . . . . . . . . . . . . . . . . . . . . 160


5 Free Klein-Gordon field theory . . . . . . . . . . . . . . . . 161
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 161
5.2 Lagrangian density . . . . . . . . . . . . . . . . . . . 163
5.3 Quantization. . . . . . . . . . . . . . . . . . . . . . . 167
5.4 Field decomposition. . . . . . . . . . . . . . . . . . . 171
5.5 Creation and annihilation operators. . . . . . . . . . 175
5.6 Energy eigenstates . . . . . . . . . . . . . . . . . . . 186
5.7 Physical meaning of energy eigenstates . . . . . . . . 190
5.8 Green’s functions . . . . . . . . . . . . . . . . . . . . 194
5.9 Covariant commutation relations . . . . . . . . . . . 205
5.10 References . . . . . . . . . . . . . . . . . . . . . . . . 209


6 Self-interacting scalar field theory . . . . . . . . . . . . . . 211
6.1 N¨other’s theorem . . . . . . . . . . . . . . . . . . . . 211
6.1.1 Space-time translation . . . . . . . . . . . . . . 215
6.2 Self-interacting φ4 theory. . . . . . . . . . . . . . . . 219
6.3 Interaction picture and time evolution operator . . . 223
6.4 S-matrix . . . . . . . . . . . . . . . . . . . . . . . . . 229
6.5 Normal ordered product and Wick’s theorem . . . . 233
6.6 Time ordered products and Wick’s theorem . . . . . 241
6.7 Spectral representation and dispersion relation . . . 246
6.8 References . . . . . . . . . . . . . . . . . . . . . . . . 254


7 Complex scalar field theory . . . . . . . . . . . . . . . . . . 257
7.1 Quantization. . . . . . . . . . . . . . . . . . . . . . . 257
7.2 Field decomposition. . . . . . . . . . . . . . . . . . . 260
7.3 Charge operator . . . . . . . . . . . . . . . . . . . . . 263
7.4 Green’s functions . . . . . . . . . . . . . . . . . . . . 268
7.5 Spontaneous symmetry breaking and the Goldstone
theorem . . . . . . . . . . . . . . . . . . . . . . . . . 270
7.6 Electromagnetic coupling. . . . . . . . . . . . . . . . 281
7.7 References . . . . . . . . . . . . . . . . . . . . . . . . 283


8 Dirac field theory. . . . . . . . . . . . . . . . . . . . . . . . 285
8.1 Pauli exclusion principle . . . . . . . . . . . . . . . . 285
8.2 Quantization of the Dirac field. . . . . . . . . . . . . 286
8.3 Field decomposition. . . . . . . . . . . . . . . . . . . 291
8.4 Charge operator . . . . . . . . . . . . . . . . . . . . . 297
8.5 Green’s functions . . . . . . . . . . . . . . . . . . . . 300
8.6 Covariant anti-commutation relations. . . . . . . . . 303
8.7 Normal ordered and time ordered products . . . . . 305
8.8 Massless Dirac fields . . . . . . . . . . . . . . . . . . 308
8.9 Yukawa interaction . . . . . . . . . . . . . . . . . . . 312
8.10 Feynman diagrams . . . . . . . . . . . . . . . . . . . 318
8.11 References . . . . . . . . . . . . . . . . . . . . . . . . 325


9 Maxwell field theory . . . . . . . . . . . . . . . . . . . . . . 327
9.1 Maxwell’s equations. . . . . . . . . . . . . . . . . . . 327
9.2 Canonical quantization . . . . . . . . . . . . . . . . . 330
9.3 Field decomposition. . . . . . . . . . . . . . . . . . . 335
9.4 Photon propagator . . . . . . . . . . . . . . . . . . . 342
9.5 Quantum electrodynamics . . . . . . . . . . . . . . . 347
9.6 Physical processes . . . . . . . . . . . . . . . . . . . . 350
9.7 Ward-Takahashi identity in QED . . . . . . . . . . . 355
9.8 Covariant quantization of the Maxwell theory . . . . 360
9.9 References . . . . . . . . . . . . . . . . . . . . . . . . 376


10 Dirac method for constrained systems . . . . . . . . . . . . 379
10.1 Constrained systems . . . . . . . . . . . . . . . . . . 379
10.2 Dirac method and Dirac bracket. . . . . . . . . . . . 384
10.3 Particle moving on a sphere . . . . . . . . . . . . . . 390
10.4 Relativistic particle . . . . . . . . . . . . . . . . . . . 395
10.5 Dirac field theory . . . . . . . . . . . . . . . . . . . . 401
10.6 Maxwell field theory . . . . . . . . . . . . . . . . . . 407
10.7 References . . . . . . . . . . . . . . . . . . . . . . . . 413


11 Discrete symmetries . . . . . . . . . . . . . . . . . . . . . . 415
11.1 Parity. . . . . . . . . . . . . . . . . . . . . . . . . . . 415
11.1.1 Parity in quantum mechanics . . . . . . . . . . 417
11.1.2 Spin zero field . . . . . . . . . . . . . . . . . . 424
11.1.3 Photon field . . . . . . . . . . . . . . . . . . . . 428
11.1.4 Dirac field . . . . . . . . . . . . . . . . . . . . . 429
11.2 Charge conjugation . . . . . . . . . . . . . . . . . . . 436
11.2.1 Spin zero field . . . . . . . . . . . . . . . . . . 437
11.2.2 Dirac field . . . . . . . . . . . . . . . . . . . . . 441
11.2.3 Majorana fermions . . . . . . . . . . . . . . . . 449
11.2.4 Eigenstates of charge conjugation . . . . . . . . 453
11.3 Time reversal . . . . . . . . . . . . . . . . . . . . . . 458
11.3.1 Spin zero field and Maxwell’s theory . . . . . . 464
11.3.2 Dirac fields . . . . . . . . . . . . . . . . . . . . 467
11.3.3 Consequences of T invariance . . . . . . . . . . 473
11.3.4 Electric dipole moment of neutron . . . . . . . 477
11.4 CPT theorem . . . . . . . . . . . . . . . . . . . . . . 479
11.4.1 Equality of mass for particles and antiparticles 479
11.4.2 Electric charge for particles and antiparticles . 480
11.4.3 Equality of lifetimes for particles and antiparticles . . . . . . . . . . . . . . . . . . . . . . . . 480
11.5 References . . . . . . . . . . . . . . . . . . . . . . . . 482


12 Yang-Mills theory . . . . . . . . . . . . . . . . . . . . . . . 485
12.1 Non-Abelian gauge theories . . . . . . . . . . . . . . 485
12.2 Canonical quantization of Yang-Mills theory . . . . . 502
12.3 Path integral quantization of gauge theories . . . . . 512
12.4 Path integral quantization of tensor fields . . . . . . 530
12.5 References . . . . . . . . . . . . . . . . . . . . . . . . 542


13 BRST invariance and its consequences . . . . . . . . . . . . 545
13.1 BRST symmetry . . . . . . . . . . . . . . . . . . . . 545
13.2 Covariant quantization of Yang-Mills theory . . . . . 550
13.3 Unitarity . . . . . . . . . . . . . . . . . . . . . . . . . 561
13.4 Slavnov-Taylor identity . . . . . . . . . . . . . . . . . 565
13.5 Feynman rules . . . . . . . . . . . . . . . . . . . . . . 571
13.6 Ghost free gauges . . . . . . . . . . . . . . . . . . . . 578
13.7 References . . . . . . . . . . . . . . . . . . . . . . . . 581


14 Higgs phenomenon and the standard model . . . . . . . . . 583
14.1 St¨uckelberg formalism . . . . . . . . . . . . . . . . . 583
14.2 Higgs phenomenon . . . . . . . . . . . . . . . . . . . 589
14.3 The standard model. . . . . . . . . . . . . . . . . . . 596
14.3.1 Field content . . . . . . . . . . . . . . . . . . . 599
14.3.2 Lagrangian density . . . . . . . . . . . . . . . . 601
14.3.3 Spontaneous symmetry breaking . . . . . . . . 605
14.4 References . . . . . . . . . . . . . . . . . . . . . . . . 616


15 Regularization of Feynman diagrams. . . . . . . . . . . . . 619
15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 619
15.2 Loop expansion . . . . . . . . . . . . . . . . . . . . . 621
15.3 Cut-off regularization . . . . . . . . . . . . . . . . . . 623
15.3.1 Calculation in the Yukawa theory . . . . . . . . 631
15.4 Pauli-Villars regularization . . . . . . . . . . . . . . . 638
15.5 Dimensional regularization . . . . . . . . . . . . . . . 647
15.5.1 Calculations in QED . . . . . . . . . . . . . . . 656
15.6 References . . . . . . . . . . . . . . . . . . . . . . . . 666


16 Renormalization theory . . . . . . . . . . . . . . . . . . . . 669
16.1 Superficial degree of divergence . . . . . . . . . . . . 669
16.2 A brief history of renormalization . . . . . . . . . . . 679
16.3 Schwinger-Dyson equation . . . . . . . . . . . . . . . 690
16.4 BPHZ renormalization . . . . . . . . . . . . . . . . . 692
16.5 Renormalization of gauge theories. . . . . . . . . . . 721
16.6 Anomalous Ward identity . . . . . . . . . . . . . . . 724
16.7 References . . . . . . . . . . . . . . . . . . . . . . . . 732


17 Renormalization group and equation . . . . . . . . . . . . . 733
17.1 Gell-Mann-Low equation . . . . . . . . . . . . . . . . 733
17.2 Renormalization group . . . . . . . . . . . . . . . . . 739
17.3 Renormalization group equation . . . . . . . . . . . . 744
17.4 Solving the renormalization group equation . . . . . 748
17.5 Callan-Symanzik equation . . . . . . . . . . . . . . . 759
17.6 References . . . . . . . . . . . . . . . . . . . . . . . . 766
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 769

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》 BOOK DETAILS 

Book nameLectures on Quantum Field Theory
AuthorsAshok Das
Useful forB.Sc / M.Sc / Ph.D / etc..
LanguageEnglish
Total Pages790 Pages
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File size8.7 MB
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