The description of the internal spaces of fermion and boson fields with "basis vectors", which are the superposition of odd and even products of the operators $γ^a$ , offers in $d=2(2n+1)$ -dimensions, such as $d=(13+1)$ , a unified picture of all so far observed fermions (quarks, leptons, antiquarks and antileptons that appear in families) and bosons (gravitons, photons, weak bosons, gluons and scalars), under the condition that all fields have non-zero angular momenta only in the $d =(3+1)$ , $SO(3,1)$ , of ordinary space-time. Bosons, which also carry the spatial index $α$ (which is for tensors and vectors $μ=(0,1,2,3)$ and for scalars $σ\ge 5$ ) appear in two orthogonal groups. In any $d=2(2n+1)$ -dimensional space the number of internal states of fermions in all families and their Hermitian conjugate partners is equal to the number of internal states of boson states. The article presents general properties of massless fermion and boson fields and their mutual interactions in this theory, which determine the Lagrangian density of both fields and their interactions. It particularly illustrates "basis vectors" and their properties in $d=(13+1)$ and $d=(5+1)$ . The article presents new results and discusses open problems in this theory.The description of the internal spaces of fermion and boson fields with "basis vectors", which are the superposition of odd and even products of the operators $γ^a$, offers in $d=2(2n+1)$-dimensions, such as $d=(13+1)$, a unified picture of all so far observed fermions (quarks, leptons, antiquarks and antileptons that appear in families) and bosons (gravitons, photons, weak bosons, gluons and scalars), under the condition that all fields have non-zero angular momenta only in the $d =(3+1)$, $SO(3,1)$, of ordinary space-time. Bosons, which also carry the spatial index $α$ (which is for tensors and vectors $μ=(0,1,2,3)$ and for scalars $σ\ge 5$) appear in two orthogonal groups. In any $d=2(2n+1)$-dimensional space the number of internal states of fermions in all families and their Hermitian conjugate partners is equal to the number of internal states of boson states. The article presents general properties of massless fermion and boson fields and their mutual interactions in this theory, which determine the Lagrangian density of both fields and their interactions. It particularly illustrates "basis vectors" and their properties in $d=(13+1)$ and $d=(5+1)$. The article presents new results and discusses open problems in this theory.

hep-thCross-listedarXiv:2512.09008Dec 10, 2025

Microscopic theory of interacting bosons

Peter A. Ring, Y. K. Gambhir, S. Iwasaki +1 more

Springer eBooksApr 6, 20082 citations

Unified Picture of Superfluidity: From Bogoliubov’s Approximation to Popov’s Hydrodynamic Theory

N. Dupuis

Using a nonperturbative renormalization-group technique, we compute the momentum and frequency dependence of the anomalous self-energy and the one-particle spectral function of two-dimensional interacting bosons at zero temperature. Below a characteristic momentum scale k_{G}, where the Bogoliubov approximation breaks down, the anomalous self-energy develops a square-root singularity and the Goldstone mode of the superfluid phase (Bogoliubov sound mode) coexists with a continuum of excitations, in agreement with the predictions of Popov's hydrodynamic theory. Thus our results provide a unified picture of superfluidity in interacting boson systems and connect Bogoliubov's theory (valid for momenta larger than k_{G}) to Popov's hydrodynamic approach.Using a nonperturbative renormalization-group technique, we compute the momentum and frequency dependence of the anomalous self-energy and the one-particle spectral function of two-dimensional interacting bosons at zero temperature. Below a characteristic momentum scale k_{G}, where the Bogoliubov approximation breaks down, the anomalous self-energy develops a square-root singularity and the Goldstone mode of the superfluid phase (Bogoliubov sound mode) coexists with a continuum of excitations, in agreement with the predictions of Popov's hydrodynamic theory. Thus our results provide a unified picture of superfluidity in interacting boson systems and connect Bogoliubov's theory (valid for momenta larger than k_{G}) to Popov's hydrodynamic approach.

arXiv:0901.4631Physical Review LettersMay 14, 200943 citations

Unified thoery of strongly correlated electron systems

Yu-Liang Liu

In framework of eigen-functional bosonization method, we introduce an imaginary phase field to uniquely represent electron correlation, and demonstrate that the Landau Fermi liquid theory and the Tomonaga-Luttinger liquid theory can be unified. It is very clear in this framework that the Tomonaga-Luttinger liquid behavior of one-dimensional interacting electron gases originates from their Fermi structure, and the non-Landau-Fermi liquid behavior of 2D interacting electron gases is induced by the long-range electron interaction, while 3D interacting electron gases generally show the Landau Fermi liquid behavior.In framework of eigen-functional bosonization method, we introduce an imaginary phase field to uniquely represent electron correlation, and demonstrate that the Landau Fermi liquid theory and the Tomonaga-Luttinger liquid theory can be unified. It is very clear in this framework that the Tomonaga-Luttinger liquid behavior of one-dimensional interacting electron gases originates from their Fermi structure, and the non-Landau-Fermi liquid behavior of 2D interacting electron gases is induced by the long-range electron interaction, while 3D interacting electron gases generally show the Landau Fermi liquid behavior.

arXiv:cond-mat/0011254Nov 15, 20000 citations

On the microscopic theory of interacting bosons

Peter A. Ring, Y. K. Gambhir, S. Iwasaki +1 more

Progress in Particle and Nuclear PhysicsJan 1, 19831 citation

The description of the internal spaces of fermion and boson fields with "basis vectors", which are the superposition of odd and even products of the operators

γ^a

, offers in

d=2(2n+1)

-dimensions, such as

d=(13+1)

, a unified picture of all so far observed fermions (quarks, leptons, antiquarks and antileptons that appear in families) and bosons (gravitons, photons, weak bosons, gluons and scalars), under the condition that all fields have non-zero angular momenta only in the

d =(3+1)

SO(3,1)

, of ordinary space-time. Bosons, which also carry the spatial index

α

(which is for tensors and vectors

μ=(0,1,2,3)

and for scalars

σ\ge 5

) appear in two orthogonal groups. In any

d=2(2n+1)

-dimensional space the number of internal states of fermions in all families and their Hermitian conjugate partners is equal to the number of internal states of boson states. The article presents general properties of massless fermion and boson fields and their mutual interactions in this theory, which determine the Lagrangian density of both fields and their interactions. It particularly illustrates "basis vectors" and their properties in

d=(13+1)

and

d=(5+1)

. The article presents new results and discusses open problems in this theory.