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Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology. One of the hallmarks…
Effective field theory methods provide a convenient approach to study static observables in field theory at finite temperature. In this talk, I will outline the construction of the effective field theory that describes effective observables…
We discuss the momentum-space topology of 3+1 and 2+1 strongly correlated fermionic systems. For the 3+1 systems the important universality class is determined by the topologically stable Fermi points in momentum space. In the extreme limit…
It is shown how quantum field theory at finite temperature can be used to set up self-consistent and gauge invariant equations for cosmological perturbations sustained by an ultrarelativistic plasma. While in the collisionless case, the…
This paper argues that the physics of condensed matter cannot be fully reduced to the supposedly fundamental quantum mechanical theory for all the atoms of which the system consists. In fact, there are many reasons to reject the idea that…
Many quantum condensed matter systems are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, topology allows us to determine generic features of their fermionic spectrum, which…
There are many possible gravitational applications of an effective approach to Quantum Field Theory (QFT) in curved space. We present a brief review of effective approach and discuss its impact for such relevant issues as the cosmological…
We derive low-energy effective field theories for the quantum anomalous Hall and topological superconducting phases. The quantum Hall phase is realized in terms of free fermions with nonrelativistic dispersion relation, possessing a global…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
Effective field theories offer a powerful method to unify diverse models under a small set of control parameters, allowing systematic expansions around well-established theories. These techniques, developed in particle physics, were…
Certain topological invariants of the moduli space of gravitational instantons are defined and studied. Several amplitudes of two and four dimensional topological gravity are computed. A notion of puncture in four dimensions, that is…
The discovery of the quantum spin Hall effect and topological insulators more than a decade ago has revolutionized modern condensed matter physics. Today, the field of topological states of matter is one of the most active and fruitful…
Trapped and cooled gases of alkali atoms can be manipulated to exhibit a variety of interesting phenomena. For example, dilute gases of fermionic atoms, in 2 hyperfine states, can be cooled to temperatures where they become superfluid. An…
We compute the exact finite temperature effective action in a 0+1-dimensional field theory containing a topological Chern-Simons term, which has many features in common with 2+1-dimensional Chern-Simons theories. This exact result explains…
The requirement of diffeomorphism symmetry for the target space can lead to anomalous commutators for the energy-momentum tensor for sigma models and for fluid dynamics, if certain topological terms are added to the action. We analyze…
Quantum cosmology implies corrections to the classical equations of motion which may lead to significant departures from the classical trajectory, especially at high curvature near the big-bang singularity. Corrections could in principle be…
Till now, the foundation of quantum physics is still mysterious. To explore the mysteries in the foundation of quantum physics, people always take it for granted that quantum processes must be some types of fields/objects on a rigid space.…
The Clifford algebra of the endomorphisms of the exterior algebra of a countably dimensional vector space induces natural bosonic shadows, i.e. families of linear maps between the cohomologies of complex grassmannians. The main result of…
Bound states of two interacting particles moving on a lattice can exhibit remarkable features that are not captured by the underlying single-particle picture. Inspired by this phenomenon, we introduce a novel framework by which genuine…
The equations for topological fields in the $4d$ higher spin theory are considered. It is shown that these fields contain a finite number of degrees of freedom that justifies their naming. The issue of construction of gauge invariant…