Narrow Results

The $V_{\mathrm{\text{lowk}}}$-renormalization group approach on the surface of Fermi liquid for nuclear matter to which Tom Kuo made a pioneering contribution at Stony Brook is found to inject the pivotal input in the formulation of the generalized nuclear effective field theory with acronym “GnEFT” applicable to superdense compact-star physics. A topology change in terms of skyrmions and half-skyrmions is shown to play the role of the “putative” hadron-quark continuity conjectured in QCD. Crucially involved are hidden local symmetry and hidden scale symmetry with the vacuum sliding with density in nuclear medium, with the nuclear tensor force emerging as a Landau Fermi-liquid fixed-point quantity. A possibly novel paradigm, a “Cheshire Catism,” in nuclear correlations is suggested.

Hidden symmetries in a covariant Hamiltonian formulation are investigated involving gauge covariant equations of motion. The special role of the Stäckel–Killing tensors is pointed out. A reduction procedure is used to reduce the original phase space to another one in which the symmetries are divided out. The reverse of the reduction procedure is done by stages performing the unfolding of the gauge transformation followed by the Eisenhart lift in connection with scalar potentials.

When hadron-quark continuity is formulated in terms of a topology change at a density higher than twice the nuclear matter density $(n_0)$, the core of massive compact stars can be described in terms of quasiparticles of fractional baryon charges, behaving neither like pure baryons nor like deconfined quarks. Hidden symmetries, both local gauge and pseudo-conformal (or broken scale), emerge and give rise both to the long-standing “effective $g_A^{\ast }\approx 1$” in nuclear Gamow–Teller (GT) transitions at $\lesssim n_0$ and to the pseudo-conformal sound velocity $v_{\mathrm{\text{pcs}}}^2/c^2\approx 1/3$ at $\gtrsim 3n_0$. It is suggested that what has been referred to, since a long time, as “quenched $g_A$” in light nuclei reflects what leads to the dilaton-limit $g_A^{\mathrm{\text{DL}}}=1$ at near the (putative) infrared fixed point of scale invariance. These properties are confronted with the recent observations in GT transitions and in astrophysical observations.

In this work, constraint conversion techniques are used to disclose the role of the second-class constraints as generator of hidden symmetries. The example of the SU(2) Skyrme model is thoroughly investigated in this approach. This study is generalized to a set of second-class surfaces of arbitrary geometries resulting from the semiclassical quantization of the collective mode of nonlinear field theories. The consequences of the hidden symmetry over the physical spectrum and the ordering ambiguity problem are explored.

It is shown that electro (magneto) static sector of Maxwell’s electrodynamics coupled to the dilaton field in a string theory form possesses the symmetry group of the stationary General Relativity in vacuum. Performing the Ernst formalism, we develope a technique for generation of exact solutions in this modified electrodynamics on the base of the normalized Ehlers symmetry transformation. In the electrostatic case, we construct and study a general class of spherically symmetric solutions that describes a pointlike source of the Coulomb type. It is demonstrated that this source is characterized by finite and singularity-free interaction at short distances. Also it is established that the total electrostatic energy of this source is finite and inversely proportional to the dilaton-Maxwell coupling constant.

I describe the long-standing search for a “smoking-gun” signal for the manifestation of (scale-)chiral symmetry in nuclear interactions. It is prompted by Gerry Brown’s last unpublished note, reproduced verbatim below, on the preeminent role of pions and vector ($\rho ,\omega$) mesons in providing a simple and elegant description of strongly correlated nuclear interactions. In this note written in tribute to Gerry Brown, I first describe a case of an unambiguous signal in axial-charge transitions in nuclei and then combine his ideas with the more recent development on the role of hidden symmetries in nuclear physics. What transpires is the surprising conclusion that the Landau–Migdal fixed point interaction $G_0^{\prime }$, the nuclear tensor forces and Brown–Rho scaling, all encoded in scale-invariant hidden local symmetry, as Gerry put, “run the show and make all forces equal.”

The inheritance of symmetries of partial differential equations occurs in a different manner from that of ordinary differential equations. In particular, the Lie algebra of the symmetries of a partial differential equation is not sufficient to predict the symmetries that will be inherited by a resulting reduced partial (or ordinary) differential equation. We show how this suggests a possible source of Type I hidden symmetries of partial differential equations as well as provide interesting consequences for solutions of partial differential equations.

I describe the long-standing search for a “smoking-gun” signal for the manifestation of (scale-)chiral symmetry in nuclear interactions. It is prompted by Gerry Brown’s last unpublished note, reproduced verbatim below, on the preeminent role of pions and vector (ρ, ω) mesons in providing a simple and elegant description of strongly correlated nuclear interactions. In this note written in tribute to Gerry Brown, I first describe a case of an unambiguous signal in axial-charge transitions in nuclei and then combine his ideas with the more recent development on the role of hidden symmetries in nuclear physics. What transpires is the surprising conclusion that the Landau–Migdal fixed point interaction $G_0^{\prime }$, the nuclear tensor forces and Brown–Rho scaling, all encoded in scale-invariant hidden local symmetry, as Gerry put, “run the show and make all forces equal.”