SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions

We propose an extension of the Yang-Mills paradigm from Lie algebras to internal chiral superalgebras. We replace the Lie algebra-valued connection one-form A, by a superalgebra-valued polyform $$ \tilde{A} $$ A ˜ mixing exterior-forms of all degrees and satisfying the chiral self-duality condition $$ \tilde{A} =^{\ast }{\tilde{A}}_{\chi } $$ A ˜ = ∗ A ˜ χ , where χ denotes the superalgebra grading operator. This superconnection contains Yang-Mills vectors valued in the even Lie subalgebra, together with scalars and self-dual tensors valued in the odd module, all coupling only to the charge parity CP-positive Fermions. The Fermion quantum loops then induce the usual Yang-Mills-scalar Lagrangian, the self-dual Avdeev-Chizhov propagator of the tensors, plus a new vector-scalar-tensor vertex and several quartic terms which match the geometric definition of the supercurvature. Applied to the SU(2/1) Lie-Kac simple superalgebra, which naturally classifies all the elementary particles, the resulting quantum field theory is anomaly-free and the interactions are governed by the super-Killing metric and by the structure constants of the superalgebra.

Double-Life Worlds

This chapter recounts the secret social lives of double lifers as they experimented with other ways of living, writing, and feeling in digital and face-to-face spaces. It describes the inescapable changes the experiments on double life wrought on exterior forms, such as on bodies and clothing, in writing or speaking. It also looks into the exterior changes of double lifers as efforts to feel more comfortable in their own skins and hints to their loved ones that they were slowly changing inside. The chapter explores the double life of Jews that are manifested in rebellious, sexualized partying in the comfort of ultra-Orthodox settings and sampling of objects, tastes, writing, and experiences based on ultra-Orthodox imaginaries of the secular world. It analyzes how double lifers pursued newfound values of autonomy, self-expression, and personal fulfilment yet stayed close to the emotional attachments of ultra-Orthodox sensibilities.

The Language of Puppetry – Code for Remembering and Theatricalization

Ever since the prehistoric age, people have been endowing some objects with symbolic status and, by animating them, they have turned them into means of communicating profound truths about man and life. The need to communicate led to conceiving a system of representation through which exterior forms of expression were created and assumed, a particular way of making the invisible visible.

Palaiologan Constantinople and a New Architectural Idiom

Following the reconquest of Constantinople in 1261, the city experienced a brief cultural revival, marked by significant works of restoration and new construction to reconnect the city to its past glory. Older monastic establishments were expanded, often with large chapels for the privileged burials of the aristocracy. The new architectural style of the period is best represented by the Church of Christ in the Chora Monastery, the best preserved project of the period, characterized by small-scale relationships in its design, picturesque asymmetries, and the lack of a clear relationship between the exterior forms and the interior spaces.

About an analogue of Neifeld’s connection on the space of centred planes with one-index basic-fibre forms

This research is realized by Cartan — Laptev method (with prolongations and scopes, moving frame and exterior forms). In this paper we consider a space П of centered m-planes (a space of all centered planes of the dimension m). This space is considered in the projective space n P . For the space П we have: dim П=n + (n – m)m. Principal fiber bundle is arised above it. The Lie group is a typical fiber of the principal fiber. This group acts in the tangent space to the П. Analogue of Neifeld’s connection with multivariate glueing is given in this fibering by Laptev — Lumiste way. The case when one-index forms are basic-fibre forms is considered. We realize an analogue of the Norden strong normalization of the space П by fields of the geometrical images: (n – m – 1)-plane which is not having the common points with a centered m-plane and (m – 1)-plane which is belonging to the m-plane and not passing through its centre. It is proved that the analog of the Norden strong normalization of the space of centered planes induces this connection.

ABOUT A CLASS OF THREE-DIMENSIONAL SUBMANIFOLDS IN AFFINE SPACE $ A^6 $

Three-dimensional submanifolds in affine space $ A^6 $ have been studied by the method of exterior forms. It is proved that the structure of total space induces a special type of affine connection on this submanifold. The structure equations of this submanifold have been found.

Seeing through the skin

This chapter is dedicated to the function of skin in artistic anatomy. Anatomy, defined as a discipline that produces knowledge about the human body via dissection, tends to cut through the skin in order to gain access to the body's interior formation. In many anatomical illustrations, the removal of skin is dramatically staged in flayed figures that are emblematic of anatomy's focus on the body's interior. For artistic practices this was increasingly seen as a problem: if the artists‘ aim was typically the representation of living human figures, then anatomical knowledge could be both a means to an end and an obstacle. Since the end of the eighteenth century, illustrated anatomical publications especially dedicated to artists paid more and more attention to the body's exterior and a new genre of text books named ‘anatomies of exterior forms‘ emerged. The chapter focuses on nineteenth-century artistic anatomies taking such a morphological approach – in particular the works by Jean-Galbert Salvage, Pierre-Nicolas Gerdy, and Julien Fau – and argues that images and texts develop a strategy of projecting anatomical knowledge onto the body's surface allowing the artist to mentally render the human skin transparent.

Nonidentical relations of skew-symmetric forms: Generation of closed exterior forms. Discrete transitions. Connection between field-theory equations and nonidentical relations

Nonidentical relations of skew-symmetric differential forms, which basis are non-integrable deforming manifolds follow from differential equations. From nonidentical relations closed exterior forms are obtained. The process of obtaining closed exterior forms describes the discrete transitions and the emergence of structures and observable formations such as waves, vertices, and turbulent pulsations. It is shown that the field theory equations (by Schroedinger, Maxwell, Einstein and others) turns to be nonidentical relations, obtained from the mathematical physics equations for material media such as the cosmologic systems, the systems of charged particles and others.

Notions of affinity in calculus of variations with differential forms

Ext-int. one affine functions are functions affine in the direction of one-divisible exterior forms with respect to the exterior product in one variable and with respect to the interior product in the other. The purpose of this article is to prove a characterization theorem for this class of functions, which plays an important role in the calculus of variations for differential forms.