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)

Objective knowledge: an evolutionary approach

We explore a new type of domain wall structure in ultrathin films with perpendicular anisotropy, that is influenced by the Dzyaloshinskii-Moriya interaction due to the adjacent layers. This study is performed by numerical and analytical micromagnetics. We show that these walls can behave like Neel walls with very high stability, moving in stationary conditions at large velocities under large fields. We discuss the relevance of such walls, that we propose to call Dzyaloshinskii domain walls, for current-driven domain wall motion under the spin Hall effect.

https://iopscience.iop.org/article/10.1209/0295-5075/100/57002/pdf

Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films

A M was supported by the King Abdullah University of Science and Technology (KAUST) T J acknowledges support from the EU FET Open RIA Grant No 766566, the Ministry of Education of the Czech Republic Grant No LM2015087 and LNSM-LNSpin, and the Grant Agency of the Czech Republic Grant No 19-28375X J S acknowledges the Alexander von Humboldt Foundation, EU FET Open Grant No 766566, EU ERC Synergy Grant No 610115, and the Transregional Collaborative Research Center (SFB/TRR) 173 SPIN+X K G and P G acknowledge stimulating discussions with C O Avci and financial support by the Swiss National Science Foundation (Grants No 200021-153404 and No 200020-172775) and the European Commission under the Seventh Framework Program (spOt project, Grant No 318144) A T acknowledges support by the Agence Nationale de la Recherche, Project No ANR-17-CE24-0025 (TopSky) J Ž acknowledges the Grant Agency of the Czech Republic Grant No 19-18623Y and support from the Institute of Physics of the Czech Academy of Sciences and the Max Planck Society through the Max Planck Partner Group programme

/pdf/current-induced-spin-orbit-torques-in-ferromagnetic-and-3tdt106r3u.pdf

Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems

Recently a Nahm transform has been discovered for magnetic bags, which are conjectured to arise in the large n limit of magnetic monopoles with charge n We interpret these ideas using string theory and present some partial proofs of this conjecture We then extend the notion of bags and their Nahm transform to higher gauge theories and arbitrary domains Bags in four dimensions conjecturally describe the large n limit of n self-dual strings We show that the corresponding Basu-Harvey equation is the large n limit of an equation describing n M2-branes, and that it has a natural interpretation in loop space We also formulate our Nahm equations using strong homotopy Lie algebras

Magnetic Domains

We propose a generalization of the Bagger-Lambert-Gustavsson action as a candidate for the description of an arbitrary number of M2-branes. The action is formulated in terms of N=2 superfields in three dimensions and corresponds to an extension of the usual superfield formulation of Chern-Simons matter theories. Demanding gauge invariance of the resulting theory does not imply the total antisymmetry of the underlying 3-Lie algebra structure constants. We relax this condition and propose a class of examples for these generalized 3-Lie algebras. We also discuss various associated ordinary Lie algebras.

Multiple M2-branes and generalized 3-Lie algebras

It was recently shown by Witten that B-type open topological string theory with the supertwistor space $\mathbb{C}P^{3|4}$ as a target space is equivalent to holomorphic Chern--Simons (hCS) theory on the same space. This hCS theory in turn is equivalent to self-dual $\mathcal{N}=4$ super-Yang–Mills (SYM) theory in four dimensions. We review the supertwistor description of self-dual and anti-self-dual $\mathcal{N}$-extended SYM theory as the integrability of SYM fields on complex $(2|\mathcal{N})$-dimensional superplanes and demonstrate the equivalence of this description to Witten's formulation. The equivalence of the field equations of hCS theory on an open subset of $\mathbb{C}P^{3|\mathcal{N}}$ to the field equations of self-dual $\mathcal{N}$-extended SYM theory in four dimensions is made explicit. Furthermore, we extend the picture to the full $\mathcal{N}=4$ SYM theory and, by using the known supertwistor description of this case, we show that the corresponding constraint equations are (gauge) equivalent to the field equations of hCS theory on a quadric in $\mathbb{C}P^{3|3}\times \mathbb{C}P^{3|3}$.

https://www.intlpress.com/site/pub/files/_fulltext/journals/atmp/2005/0009/0006/ATMP-2005-0009-0006-a002.pdf

On supertwistors, the Penrose-Ward transform and N=4 super Yang-Mills theory

We review in detail the Batalin-Vilkovisky formalism for Lagrangian field theories and its mathematical foundations with an emphasis on higher algebraic structures and classical field theories. In particular, we show how a field theory gives rise to an $L_\infty$-algebra and how quasi-isomorphisms between $L_\infty$-algebras correspond to classical equivalences of field theories. A few experts may be familiar with parts of our discussion, however, the material is presented from the perspective of a very general notion of a gauge theory. We also make a number of new observations and present some new results. Most importantly, we discuss in great detail higher (categorified) Chern-Simons theories and give some useful shortcuts in usually rather involved computations.

$L_\infty$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism

We develop an analytical approach to scalar field theory on the fuzzy sphere based on considering a perturbative expansion of the kinetic term. This expansion allows us to integrate out the angular degrees of freedom in the hermitian matrices encoding the scalar field. The remaining model depends only on the eigenvalues of the matrices and corresponds to a multitrace hermitian matrix model. Such a model can be solved by standard techniques as e.g. the saddle-point approximation. We evaluate the perturbative expansion up to second order and present the one-cut solution of the saddle-point approximation in the large N limit. We apply our approach to a model which has been proposed as an appropriate regularization of scalar field theory on the plane within the framework of fuzzy geometry.

https://iopscience.iop.org/article/10.1088/1126-6708/2007/08/066/pdf

Christian Saemann

Papers

Magnetic Domains

Multiple M2-branes and generalized 3-Lie algebras

On supertwistors, the Penrose-Ward transform and N=4 super Yang-Mills theory

$L_\infty$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism

Fuzzy scalar field theory as a multitrace matrix model