Wave function of the photon in a curved spacetime

It is known that the classical variables are replaced by operators for the dynamics of the electromagnetic field, thus the second quantization is traditionally used. There is a significant question in modern theoretical physics area: “Why is there no fully developed first-quantized theory of photons?” In the present work, we argue that a photon wave function can be obtained if one uses the massless Duffin-Kemmer-Petiau (mDKP) equation. Thus, we focus on exact solutions of the mDKP equation the Robertson–Walker type spacetime via the Teleparallel Theory (TPT) of Gravity. The mDKP equation is generally known as the spinor formulation of the photons. We also focus on solutions of the Maxwell equations (MEs) to verify the equivalence between the mDKP and the ME formulations of the photons. It is shown that photons present an oscillatory behavior.

Two-loop superstring five-point amplitudes. Part I. Construction via chiral splitting and pure spinors

The full two-loop amplitudes for five massless states in Type II and Heterotic superstrings are constructed in terms of convergent integrals over the genus-two moduli space of compact Riemann surfaces and integrals of Green functions and Abelian differentials on the surface. The construction combines elements from the BRST cohomology of the pure spinor formulation and from chiral splitting with the help of loop momenta and homology invariance. The α′ → 0 limit of the resulting superstring amplitude is shown to be in perfect agreement with the previously known amplitude computed in Type II supergravity. Investigations of the α′ expansion of the Type II amplitude and comparisons with predictions from S-duality are relegated to a first companion paper. A construction from first principles in the RNS formulation of the genus-two amplitude with five external NS states is relegated to a second companion paper.

Advantage of the second-order formalism in double space T-dualization of type II superstring

In this article we present bosonic T-dualization in double space of the type II superstring theory in the pure spinor formulation. We use the action with constant background fields obtained from the general case under some physically and mathematically justified assumptions. Unlike Nikolić and Sazdović (EPJ C 77:197, 2017), where we used the first-order theory, in this article fermionic momenta are integrated out. Full T-dualization in double space is represented as a permutation of the initial $$x^\mu $$xμ and T-dual coordinates $$y_\mu $$yμ. Requiring that a T-dual transformation law of the T-dual double coordinate $${}^\star Z^M=(y_\mu ,x^\mu )$$⋆ZM=(yμ,xμ) to be of the same form as for initial one $$Z^M=(x^\mu ,y_\mu )$$ZM=(xμ,yμ), we obtain the form of the T-dual background fields in terms of the initial ones. The advantage of using the action with integrated fermionic momenta is that it gives all T-dual background fields in terms of the initial ones. In the case of the first-order theory Nikolić and Sazdović (2017) a T-dual R-R field strength was obtained out of the double space formalism under additional assumptions.

CORRELATION FUNCTIONS IN BERKOVITS' PURE SPINOR FORMULATION

We use Berkovits' pure spinor quantization to compute various three-point tree correlation functions in position-space for the Type IIB superstring. We solve the constraint equations for the vertex operators and obtain explicit expressions for the graviton and axion components of the vertex operators. Using these operators we compute tree level correlation functions in flat space and discuss their extension to the AdS5 × S5 background.