The quantum Fisher information (QFI) of the vacuum of three quantum field theories is evaluated with respect to the mass parameter of each theory. All field theories are considered on a $(d+1)$ -dimensional Euclidean spacetime. We consider the Klein-Gordon field and the free Dirac field. For the free KG case, we find a $m^{d-2}$ dependence of the QFI, and thus no dependence for $d=2$ , in agreement with the holographic duality characterizing the theory. The vacuum QFI with respect to the free Dirac field mass is shown to be UV-divergent for $d=2$ and $d=3$ , mass-dependent for $d=1$ , and zero for $d=0$ .The quantum Fisher information (QFI) of the vacuum of three quantum field theories is evaluated with respect to the mass parameter of each theory. All field theories are considered on a $(d+1)$-dimensional Euclidean spacetime. We consider the Klein-Gordon field and the free Dirac field. For the free KG case, we find a $m^{d-2}$ dependence of the QFI, and thus no dependence for $d=2$, in agreement with the holographic duality characterizing the theory. The vacuum QFI with respect to the free Dirac field mass is shown to be UV-divergent for $d=2$ and $d=3$, mass-dependent for $d=1$, and zero for $d=0$.

hep-thCross-listedarXiv:2607.26919Jul 30, 2026

Quantum Field Theory

H.-J. Unger

Zeitschrift für Physikalische ChemieJan 1, 19940 citations

Quantum Field Theory

Armin Uhlmann

Zeitschrift für Physikalische ChemieJan 1, 19960 citations

Spin operator and spin states in Galilean covariant Fermi field theories

Fuad M. Saradzhev

Spin degrees of freedom of the Galilean covariant Dirac field in $(4+1)$ dimensions and its nonrelativistic counterpart in $(3+1)$ dimensions are examined. Two standard choices of spin operator, the Galilean covariant and Dirac spin operators, are considered. It is shown that the Dirac spin of the Galilean covariant Dirac field in $(4+1)$ dimensions is not conserved, and the role of non-Galilean boosts in its nonconservation is stressed out. After reduction to $(3+1)$ dimensions the Dirac field turns into a nonrelativistic Fermi field with a conserved Dirac spin. A generalized form of the L\'evy-Leblond equations for the Fermi field is given. One-particle spin states are constructed. A particle-antiparticle system is discussed.Spin degrees of freedom of the Galilean covariant Dirac field in $(4+1)$ dimensions and its nonrelativistic counterpart in $(3+1)$ dimensions are examined. Two standard choices of spin operator, the Galilean covariant and Dirac spin operators, are considered. It is shown that the Dirac spin of the Galilean covariant Dirac field in $(4+1)$ dimensions is not conserved, and the role of non-Galilean boosts in its nonconservation is stressed out. After reduction to $(3+1)$ dimensions the Dirac field turns into a nonrelativistic Fermi field with a conserved Dirac spin. A generalized form of the L\'evy-Leblond equations for the Fermi field is given. One-particle spin states are constructed. A particle-antiparticle system is discussed.

arXiv:1109.4899Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsDec 20, 20112 citations

The quantum Fisher information (QFI) of the vacuum of three quantum field theories is evaluated with respect to the mass parameter of each theory. All field theories are considered on a

(d+1)

-dimensional Euclidean spacetime. We consider the Klein-Gordon field and the free Dirac field. For the free KG case, we find a

m^{d-2}

dependence of the QFI, and thus no dependence for

d=2

, in agreement with the holographic duality characterizing the theory. The vacuum QFI with respect to the free Dirac field mass is shown to be UV-divergent for

d=2

and

d=3

, mass-dependent for

d=1

, and zero for

d=0

Spin degrees of freedom of the Galilean covariant Dirac field in

(4+1)

dimensions and its nonrelativistic counterpart in

(3+1)

dimensions are examined. Two standard choices of spin operator, the Galilean covariant and Dirac spin operators, are considered. It is shown that the Dirac spin of the Galilean covariant Dirac field in

(4+1)

dimensions is not conserved, and the role of non-Galilean boosts in its nonconservation is stressed out. After reduction to

(3+1)

dimensions the Dirac field turns into a nonrelativistic Fermi field with a conserved Dirac spin. A generalized form of the L\'evy-Leblond equations for the Fermi field is given. One-particle spin states are constructed. A particle-antiparticle system is discussed.