To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

Superstring theoryをめぐって(放談室)

Non-perturbative renormalization flow in quantum field theory and statistical physics

The zero modes of closed strings on a torus — the torus coordinates plus dual coordinates conjugate to winding number — parameterize a doubled torus. In closed string field theory, the string field depends on all zero-modes and so can be expanded to give an infinite set of fields on the doubled torus. We use string field theory to construct a theory of massless fields on the doubled torus. Key to the consistency is a constraint on fields and gauge parameters that arises from the L0−0 = 0 condition in closed string theory. The symmetry of this double field theory includes usual and `dual diffeomorphisms', together with a T-duality acting on fields that have explicit dependence on the torus coordinates and the dual coordinates. We find that, along with gravity, a Kalb-Ramond field and a dilaton must be added to support both usual and dual diffeomorphisms. We construct a fully consistent and gauge invariant action on the doubled torus to cubic order in the fields. We discuss the challenges involved in the construction of the full nonlinear theory. We emphasize that the doubled geometry is physical and the dual dimensions should not be viewed as an auxiliary structure or a gauge artifact.

Double Field Theory

Vorlesungen uber theoretische Physik Von Prof. Arnold Sommerfeld. Band 1: Mechanik. Vierte, neubearbeitete Auflage. Pp. xii + 276. 18 D. marks. Band 2: Mechanik der deformierbaren Medien. Pp. xv + 376 + 4 plates. 18 D. marks. Band 3: Elektrodynamik. Pp. xvi + 368. 18 D. marks. Band 6: Partielle Differentialgleichungen der Physik. Pp. xiii + 332. 18 D. marks. (Wiesbaden: Dieterich'sche Verlagsbuchhandlung, 1947–1949.)

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Lectures on Theoretical Physics

We construct a gauge-invariant regularisation scheme for pure SU(N) Yang–Mills theory in dimension four or less (for N = ∞ in all dimensions), with a physical cutoff scale Λ, by using covariant higher derivatives and spontaneously broken SU(N|N) supergauge invariance. Providing their powers are within certain ranges, the covariant higher derivatives cure the superficial divergence of all but a set of one-loop graphs. The finiteness of these latter graphs is ensured by properties of the supergroup and gauge invariance. In the limit Λ → ∞, all the regulator fields decouple and unitarity is recovered in the renormalized pure SU(N) Yang–Mills theory. By demonstrating these properties, we prove that the regularisation works to all orders in perturbation theory.

Gauge invariant regularisation via SU(N|N)

We derive the second variation Lagrangian of the Randall–Sundrum model with two branes, study its gauge invariance and diagonalize it in the unitary gauge. We also show that the effective four-dimensional theory looks different on different branes and calculate the observable mass spectra and the couplings of the physical degrees of freedom of five-dimensional gravity to matter.

Effective Lagrangians for physical degrees of freedom in the Randall–Sundrum model

Gradient Flows From An Approximation To The Exact Renormalization Group

Effective Potential and KK-Renormalization Scheme in a 5D Supersymmetric Theory

We construct the second variation Lagrangian for Randall-Sundrum model with two branes, study its gauge invariance, find the corresponding equations of motion and decouple them. We also derive an effective Lagrangian for this model in the unitary gauge, which describes a massless graviton, massive gravitons and a massless scalar radion. It is shown that the mass spectra of these fields and their couplings to the matter are different on different branes.

Yuri Kubyshin

Papers

Gauge invariant regularisation via SU(N|N)

Effective Lagrangians for physical degrees of freedom in the Randall–Sundrum model

Gradient Flows From An Approximation To The Exact Renormalization Group

Effective Potential and KK-Renormalization Scheme in a 5D Supersymmetric Theory

Effective Lagrangians for linearized gravity in Randall-Sundrum model