This graduate-level book is a coherent and self-contained introduction to quantum field theory (QFT), with a distinctive focus on geometric and nonperturbative aspects. The opening part covers quantum fields and the Euclidean path integral, Yang–Mills field theories, and Wilsonian renormalization. Wilson's notion of the effective field theory and its heavy implication for the QFT framework itself are given particular attention. Next, geometric and topological aspects are thoroughly treated, accompanied by a healthy dose of underlying mathematics. Anomalies—quantum failures of classical symmetries—follow as crucial litmus tests for self-consistency, which are delineated in unprecedented detail, spanning decades of development. In the final part, the book asks how relativistic gravity, known to resist standard quantization schemes, may be reconciled with the quantum world. This question is approached by invoking the d = 2 Weyl anomaly, Hawking effects, black hole partition functions, and the renormalization of fundamental strings, with a view toward superstring theory.
These notes are aimed at providing a relatively concise and self-contained introduction to anomalies in quantum field theory. A first part reviews the necessary notions of quantum field theory, in particular its functional integral formulation which we use throughout. Then we discuss in some detail how and why anomalie...
This paper extends the Schrödinger quantum field—a wave function treated as a fundamental quantum field describing particle states and probabilities—to a fully relativistic framework within Parametrized Relativistic Quantum Theory (PRQT). A hallmark of parametrized theories is the use of an invariant evolution paramete...
J. Fanchi· American Journal of Physics· 0 citations
Quantum field theory (QFT) and general relativity are individually successful but hard to reconcile. The holographic principle, realized concretely in the AdS/CFT correspondence, offers a route to a reconciliation. However, this correspondence is rigorously established only for special, highly supersymmetric string the...
The quantum geometric tensor - the Berry curvature together with the quantum metric - now underlies a long list of observables, from the anomalous Hall effect to the superfluid weight of a flat band. We ask which of these observables actually require quantum mechanics. To answer this question, we study a purely classic...
This is an English translation of a book originally published in Japanese by Saiensu-sha in 2015. The book is an introduction to the 3d-3d correspondence, the relation between 3d $\mathcal{N}=2$ supersymmetric gauge theories and the geometry of 3-manifolds, which arises from the compactification of the 6d $\mathcal{N}=...
The geometry of quantum states is a fundamental research area with applications ranging from band theory in condensed matter to variational algorithms in quantum information. Due to their relative simplicity, pure states are usually studied, while mixed ones are needed in general, for instance to allow for finite tempe...
Per Moosavi· 0 citations
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