109,866 research outputs found

    Locally covariant quantum field theory with external sources

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    We provide a detailed analysis of the classical and quantized theory of a multiplet of inhomogeneous Klein-Gordon fields, which couple to the spacetime metric and also to an external source term; thus the solutions form an affine space. Following the formulation of affine field theories in terms of presymplectic vector spaces as proposed in [Annales Henri Poincare 15, 171 (2014)], we determine the relative Cauchy evolution induced by metric as well as source term perturbations and compute the automorphism group of natural isomorphisms of the presymplectic vector space functor. Two pathological features of this formulation are revealed: the automorphism group contains elements that cannot be interpreted as global gauge transformations of the theory; moreover, the presymplectic formulation does not respect a natural requirement on composition of subsystems. We therefore propose a systematic strategy to improve the original description of affine field theories at the classical and quantized level, first passing to a Poisson algebra description in the classical case. The idea is to consider state spaces on the classical and quantum algebras suggested by the physics of the theory (in the classical case, we use the affine solution space). The state spaces are not separating for the algebras, indicating a redundancy in the description. Removing this redundancy by a quotient, a functorial theory is obtained that is free of the above mentioned pathologies. These techniques are applicable to general affine field theories and Abelian gauge theories. The resulting quantized theory is shown to be dynamically local.Comment: v2: 42 pages; Appendix C on deformation quantization and references added. v3: 47 pages; compatible with version to appear in Annales Henri Poincar

    Quantum Field Theory

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    I discuss the general principles underlying quantum field theory, and attempt to identify its most profound consequences. The deepest of these consequences result from the infinite number of degrees of freedom invoked to implement locality. I mention a few of its most striking successes, both achieved and prospective. Possible limitations of quantum field theory are viewed in the light of its history.Comment: LaTeX, 12 pages, 3 figures. Will appear in Centenary issue of Rev. of Mod. Phys., March 1999. Incorporated minor corrections suggested by edito

    Constructive Quantum Field Theory

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    A review of the renormalization group approach to the proof of non perturbative ultraviolet stability in scalar field theories in dimension d=2,3.Comment: Plain Te

    Relative quantum field theory

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    We highlight the general notion of a relative quantum field theory, which occurs in several contexts. One is in gauge theory based on a compact Lie algebra, rather than a compact Lie group. This is relevant to the maximal superconformal theory in six dimensions.Comment: 19 pages, 4 figures; v2 small changes for publication; v3 small final changes for publicatio

    Braided Quantum Field Theory

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    We develop a general framework for quantum field theory on noncommutative spaces, i.e., spaces with quantum group symmetry. We use the path integral approach to obtain expressions for nn-point functions. Perturbation theory leads us to generalised Feynman diagrams which are braided, i.e., they have non-trivial over- and under-crossings. We demonstrate the power of our approach by applying it to Ï•4\phi^4-theory on the quantum 2-sphere. We find that the basic divergent diagram of the theory is regularised.Comment: 31 pages, LaTeX with AMS and XY-Pic macros; final version to appear in Commun. Math. Phy

    Euclidean Field Theory

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    A coincise review about Euclidean (Quantum) Field Theory is presented. It deals with the general structural properties, the connections with Quantum Field Theory, the exploitation in Constructive Quantum Field Theory, and the physical interpretation.Comment: 19 page
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