## Research Interests

**Horizon Mass Theorem (2005)**

For all black holes: neutral, charged or rotating, the horizon mass is always equal to twice the irreducible mass observed at infinity.

**Bosonization Theorem (2014)**

For any Lagrangian invariant under U(1) symmetry transformation in two dimensions, if the chiral fermion is the group element, then the chiral boson is the group parameter and vice versa.

**General Relativity and Black Holes**

In recent years, there has been a greater connection between traditional particle physics and astrophysics than that from thirty years ago. Black holes are of fundamental importance in theoretical physics and in cosmology. I have found a new theorem for black holes known as the Horizon Mass Theorem. The theorem is important for extending the Second Law of Thermodynamics to include gravitation. Because of the validity of this theorem: the horizon mass being greater than its asymptotic mass, a black hole can therefore emit radiation according to the idea of Hawking. The theorem also implies that for a black hole in the most general case, there are no electric charges or physical rotations inside the black hole. The electrostatic energy and the rotational energy of a black hole are all external quantities. This is a surprising result and it could help to understand various particle processes near the horizon of a black hole and to answer questions about the quantum nature of black holes such as the firewall paradox and the information loss problem.

**Quantum Gravity**

But the most fundamental problem in theoretical physics in the 21st Century is quantum gravity. What is the nature of quantum gravity and what are the physical phenomena? Does gravity merely exist with other quantum theories or is there a deeper connection between the two subjects? Many quantum gravity theories have been proposed but none has so far been successful. The difficulty appears to be created by insisting on a conventional quantum field theory approach. Currently, I am investigating gravity by considering classical gravity to be a derived interaction from an underlying theory. This underlying theory would involve new degrees of freedom at a deeper level and it would be structurally different from classical gravitation. It may conceivably be a quantum theory or a non-quantum theory, and a non-quantum approach does not mean it is classical. The relation between this underlying theory and Einstein’s gravity is then similar to the connection between statistical mechanics and thermodynamics. This may offer a radical new direction to unify all the forces in Nature.

**Quantum Field Theory**

Another area of my research is in quantum field theory. In particular, the focus is on quantum symmetries and completely integrable systems. I have established a concise quantum operator formula for bosonization in which the Lie group structure appears in a natural way. Bosonization is an extraordinary way of expressing a fermion field theory in terms of a boson field theory in two dimensions. The connection between fermions and bosons is found to be exactly the connection between Lie group elements and the group parameters. All the properties of the fermion field theory are shown to be preserved under this remarkable transformation with substantial simplification and elucidation of the original theory, much like Lie groups can be studied effectively by their Lie algebras. As a result, bosonization has become a novel symmetry operation in quantum field theory and it is used to uncover unexpected new quantum symmetries and interactions in two dimensions.

## Key Publications

Y.K. Ha, An Underlying Theory for Gravity, J. Phy. Conf. Ser. 484 (2014) 012061

Y.K. Ha, Severe Challenges in Gravity Theories, Int. J. Mod. Phy. Conf. Ser. Vol. 7, 219- 226 (2012)

Y.K. Ha, Is There Unification in the 21st Century? , Proceedings of the Conference in Honour of Murray Gell-Mann’s 80th Birthday, 496-502 (World Scientific 2011)

Y.K. Ha, Are Black Holes Elementary Particles? , Int. J. Mod. Phy. A, Vol. 24, 3677-3583 (2009)

Y.K. Ha, A New Theorem for Black Holes, Proceedings of XXVI International Colloquium on Group Theoretical Methods in Physics, New York (2006)

Y.K. Ha, Horizon Mass Theorem, Int. J. Mod. Phy. D, Vol. 14, 2219-2225 (2005) (Gravity Research Foundation Award)

Y.K. Ha, The Gravitational Energy of a Black Hole, Gen. Rel. Grav., Vol. 35, 2045-2050 (2003)

Y.K. Ha, Coupling of Gravity to Matter via SO(3,2) Gauge Fields, Gen. Rel. Grav., Vol. 27, 713-719 (1995)

Y.K. Ha, Non-compact Symmetries in Field Theories with Indefinite Metric, Nucl. Phys. B, Vol. 256, 687-704 (1985)

Y.K. Ha, Boson Formulation of Fermion Field Theories, Phys. Rev. D, Vol. 29, 1744-1756 (1984)

Y.K. Ha, Severe Challenges in Gravity Theories, Int. J. Mod. Phy. Conf. Ser. Vol. 7, 219- 226 (2012)

Y.K. Ha, Is There Unification in the 21st Century? , Proceedings of the Conference in Honour of Murray Gell-Mann’s 80th Birthday, 496-502 (World Scientific 2011)

Y.K. Ha, Are Black Holes Elementary Particles? , Int. J. Mod. Phy. A, Vol. 24, 3677-3583 (2009)

Y.K. Ha, A New Theorem for Black Holes, Proceedings of XXVI International Colloquium on Group Theoretical Methods in Physics, New York (2006)

Y.K. Ha, Horizon Mass Theorem, Int. J. Mod. Phy. D, Vol. 14, 2219-2225 (2005) (Gravity Research Foundation Award)

Y.K. Ha, The Gravitational Energy of a Black Hole, Gen. Rel. Grav., Vol. 35, 2045-2050 (2003)

Y.K. Ha, Coupling of Gravity to Matter via SO(3,2) Gauge Fields, Gen. Rel. Grav., Vol. 27, 713-719 (1995)

Y.K. Ha, Non-compact Symmetries in Field Theories with Indefinite Metric, Nucl. Phys. B, Vol. 256, 687-704 (1985)

Y.K. Ha, Boson Formulation of Fermion Field Theories, Phys. Rev. D, Vol. 29, 1744-1756 (1984)