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電子ブック
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1. Combinatorial physics : combinatorics, quantum field theory, and quantum gravity models (: electronic bk)
Adrian Tanasa
出版情報: [Oxford] : Oxford University Press, [20--]  1 online resource
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目次情報: 続きを見る
Introduction / 1：
Graphs, ribbon graphs, and polynomials / 2：
Graph theory: The Tutte polynomial / 2.1：
Ribbon graphs; the Bollobás-Riordan polynomial / 2.2：
Selected further reading / 2.3：
Quantum field theory (QFT)-built-in combinatorics / 3：
Definition of the scalar ¿4 model / 3.1：
Perturbative expansion-Feynman graphs and their combinatorial weights / 3.2：
Fourier transform-the momentum space / 3.3：
Parametric representation of Feynman integrands / 3.4：
The propagator and the heat kernel / 3.5：
A glimpse of perturbative renormalization / 3.6：
The power counting theorem / 3.6.1：
Locality / 3.6.2：
Multi-scale analysis / 3.6.3：
The subtraction operator for a general Feynman graph / 3.6.4：
Dimensional renormalization / 3.6.5：
Dyson-Schwinger equation / 3.7：
Combinatorial (or 0-dimensional) QFT and the intermediate field method / 3.8：
Combinatorial (or 0-dimensionai) QFT / 3.8.1：
The intermediate field method / 3.8.2：
Tree weights and renormalization in QFT / 3.9：
Preliminary results / 4.1：
Partition tree weights / 4.2：
Combinatorial QFT and the Jacobian Conjecture / 4.3：
The Jacobian Conjecture as combinatorial QFT model (the Abdesselam-Rivasseau model) / 5.1：
The intermediate field method for the Abdesselam-Rivasseau model / 5.2：
Fermionic QFT, Grassmann calculus, and combinatorics / 5.3：
Grassmann algebras and Grassmann calculus / 6.1：
The Grassmann algebra / 6.1.1：
Grassmann calculus; Pfaffians as Grassmann integrals / 6.1.2：
On Grassmann Gaussian measures / 6.2：
Lingström-Gessel-Viennot (LGV) formula for graphs with cycles / 6.3：
Stembridge's formulas for graphs with cycles / 6.4：
A generalization / 6.5：
Tutte polynomial and the parametric representation in QFT / 6.6：
Analytic combinatorics and QFT / 6.7：
The Mellin transform technique / 7.1：
The saddle point method / 7.2：
Algebraic combinatorics and QFT / 7.3：
Algebraic reminder; Combinatorial Hopf Algebras (CHAs) / 8.1：
The Connes-Kreimer Hopf algebra of Feynman graphs / 8.2：
The B+ operator, Hochschild cohomology of the Connes-Kreimer algebra / 8.3：
Multi-scale renormaiizarion, CHA description / 8.4：
QFT on the non-commutative Moyal space and combinatorics / 8.5：
Mathematical setting: Renormalizability / 9.1：
The Mehler kernel and the Grosse-Wulkenhaar model / 9.2：
Parametric representation of Grosse-Wulkenhaar-like models / 9.3：
The Mellin transform and the Grosse-Wulkenhaar model / 9.4：
Dimensional renormalization for the Grosse-Wulkenhaar model / 9.5：
A heat kernel-based renormalizable model / 9.6：
Parametric representation and the Bollobás-Riordan polynomial / 9.7：
Parametric representation / 9.7.1：
Relation between the multi-variate Bollobás-Riordan and the polynomials of the parametric representation / 9.7.2：
Combinatorial Connes-Kreimer Hopf algebra and its Hochschild cohomology / 9.8：
Combinatorial Connes-Kreimer Hopf algebra / 9.8.1：
Hochschild cohomology and the combinatorial DSE / 9.8.2：
Quantum gravity, group field theory (GFT), and combinatorics / 9.9：
Quantum gravity / 10.1：
Main candidates for a theory of quantum gravity: The holographic principle / 10.2：
GFT models: the Boulatov and the colourable models / 10.3：
The multi-orientable GFT model / 10.4：
Tadpoles and generalized tadpoles / 10.4.1：
Tadfaces / 10.4.2：
Saddle point method for GFT Feynman integrals / 10.5：
Algebraic combinatorics and tensorial GFT / 10.6：
The Ben Geloun-Rivasseau (BGR) model / 10.6.1：
Cones-Kreimer Hopf algebraic description of the combinatorics of the renormalizability of the BGR model / 10.6.2：
Hochschild cohomology and the combinatorial DSE for tensorial GFT / 10.6.3：
From random matrices to random tensors / 10.7：
The large N limit / 11.1：
The double-scaling limit / 11.2：
From matrices to tensors / 11.3：
Tensor graph polynomials-a generalization of the Bollobás-Riordan polynomial / 11.4：
Random tensor models-the U(N)D-invariant model / 11.5：
Definition of the model and its DSE / 12.1：
U(N)D-invariant bubble interactions / 12.1.1：
Bubble observables / 12.1.2：
The DSE for the model / 12.1.3：
Navigating the following sections of the chapter / 12.1.4：
The DSE beyond the large N limit / 12.2：
The LO / 12.2.1：
Moments and Cumulants / 12.2.2：
Gaussian and non-Gaussian contributions / 12.2.3：
The DSE at NLO / 12.2.4：
The order 1/ND in the quartic model / 12.2.5：
Double-scaling limit in the DSE / 12.3：
From the quartic model to a generic model / 12.3.2：
Random tensor models-the multi-orientable (MO) model / 12.4：
Definition of the model / 13.1：
The 1/N expansion and the large N limit / 13.2：
Feynman amplitudes; the 1/N expansion / 13.2.1：
The large N limit-the LO (melonic graphs) / 13.2.2：
The large TV limit-the NLO / 13.2.3：
Leading and NLO series / 13.2.4：
Combinatorial analysis of the general term of the large N expansion / 13.3：
Dipoles, chains, schemes, and all that / 13.3.1：
Generating functions, asymptotic enumeration, and dominant schemes / 13.3.2：
The two-point function / 13.4：
The four-point function / 13.4.2：
The 2r-point function / 13.4.3：
Random tensor models-the O(N)3-invariant model / 13.5：
General model and large N expansion / 14.1：
Quartic model, large N expansion / 14.2：
Large N expansion: LO / 14.2.1：
NLO / 14.2.2：
General quartic model: Critical behaviour / 14.3：
Explicit counting of melonic graphs / 14.3.1：
Diagrammatic equations, LO and NLO / 14.3.2：
Singularity analysis / 14.3.3：
Critical exponents / 14.3.4：
The Sachdev-Ye-Kitaev (SYK) holographic model / 14.4：
Definition of the SYK model: Its Feynman graphs / 15.1：
Diagrammatic proof of the large N melonic dominance / 15.2：
The coloured SYK model / 15.3：
Definition of the model, real, and complex versions / 15.3.1：
Diagrammatics of the real and complex model / 15.3.2：
More on the coloured SYK Feynman graphs / 15.3.3：
Non-Gaussian disorder average in the complex model / 15.3.4：
SYK-like tensor models / 15.4：
The Gurau-Witten model and its diagrammatics / 16.1：
Two-point functions: LO, NLO, and so on / 16.1.1：
Four-point function: LO, NLO, and so on / 16.1.2：
The O(N)3-invariant SYK-Uke tensor model / 16.2：
The MO SYK-like tensor model / 16.3：
Relating MO graphs to O(N)3-invariant graphs / 16.4：
Diagrammatic techniques for O(N)3-invariant graphs / 16.5：
Two-edge-cuts / 16.5.1：
Dipole removals / 16.5.2：
Dipole insertions / 16.5.3：
Chains of dipoles / 16.5.4：
Face length / 16.5.5：
The strategy / 16.5.6：
Degree 1 graphs of the O(N)3-invariant SYK-like tensor model / 16.6：
2PI, dipole-free graph of degree one / 16.6.1：
The graphs of degree 1 / 16.6.2：
Degree 3/2 graphs of the O(N)3-invariant SYK-like tensor model / 16.7：
Examples of tree weights / A：
Symmetric weights-complete partition / A.1：
One singleton partition-rooted graph / A.2：
Two singleton partition-multi-rooted graph / A.3：
Renormalization of the Grosse-Wulkenhaar model, one-loop examples / B：
The B+ operator in Moyal QFT, two-loop examples / C：
One-loop analysis / C.1：
Two-loop analysis / C.2：
Explicit examples of GFT tensor Feynman integral computations / D：
A non-colourable, MO tensor graph integral / D.1：
A colourable, multi-orientable tensor graph integral / D.2：
A non-colourable, non-multi-orientable tensor graph integral / D.3：
Coherent states of SU(2) / E：
Proof of the double-scaling limit of the U(N)D-invariant tensor model / F：
Proof of Theorem 15.3.2 / G：
Bijection with constellations / G.1：
Bijection in the bipartite case / G.1.1：
The non-bipartite case / G.1.2：
Enumeration of coloured graphs of fixed order / G.2：
Exact enumeration / G.2.1：
The connectivity condition and SYK graphs / G.2.2：
Preliminary conditions / G.3.1：
The case q > 3 / G.3.2：
The case q = 3 / G.3.3：
Proof of Theorem 16.1.1 / G.3.4：
Summary of results on the diagrammatics of the coloured SYK model and of the Gurau-Witten model / I：
Bibliography
Index
Introduction / 1：
Graphs, ribbon graphs, and polynomials / 2：
Graph theory: The Tutte polynomial / 2.1：
2.

電子ブック
ＥＢ
2. Quantum theory : an information processing approach (: electronic bk)
Jochen Rau
出版情報: [Oxford] : Oxford University Press, [20--]  1 online resource
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電子ブック
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3. Crafting the quantum : Arnold Sommerfeld and the practice of theory, 1890-1926 (: electronic bk)
Suman Seth
出版情報: [Ann Arbor, Mich.] : ProQuest Ebook Central, [20--]  1 online resource (viii, 378 p.)
シリーズ名: Transformations : studies in the history of science and technology
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Acknowledgments
Introduction
The Physics of Problems / I：
Elements of the Sommerfeld Style, 1890-1910
Pedagogical Economies / 2：
The "Sommerfeld School" and the Problems of Teaching
The Kaiser's Physicists / 3：
The Sommerfeld School Goes to War
The Practice of Principles / II：
Planck, Experiment, and the "Thermodynamic Method"
The Dynamical and the Statistical / 5：
Sommerfeld, Planck, and the Quantum Hypothesis
Prinzipienfuchser and Virtuosen / III：
Theoretical Physics after World War I
Crafting the Quantum / 7：
Sommerfeld, Bohr, and the Older Quantum Theory
Conclusion
Notes
Bibliography
Index
Acknowledgments
Introduction
The Physics of Problems / I：
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