What is Coupling constants: Definition and 17 Discussions
In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between two static bodies to the "charges" of the bodies (i.e. the electric charge for electrostatic and the mass for Newton's gravity) divided by the distance squared,
r
2
{\displaystyle r^{2}}
, between the bodies; thus: G in
F
=
G
M
m
/
r
2
{\displaystyle F=GMm/r^{2}}
for Newton's gravity and
k
e
{\displaystyle k_{\text{e}}}
in
F
=
k
e
q
1
q
2
/
r
2
{\displaystyle F=k_{\text{e}}q_{1}q_{2}/r^{2}}
for electrostatic. This description remains valid in modern physics for linear theories with static bodies and massless force carriers.
A modern and more general definition uses the Lagrangian
L
{\displaystyle {\mathcal {L}}}
(or equivalently the Hamiltonian
H
{\displaystyle {\mathcal {H}}}
) of a system. Usually,
L
{\displaystyle {\mathcal {L}}}
(or
H
{\displaystyle {\mathcal {H}}}
) of a system describing an interaction can be separated into a kinetic part
T
{\displaystyle T}
and an interaction part
V
{\displaystyle V}
:
L
=
T
−
V
{\displaystyle {\mathcal {L}}=T-V}
(or
H
=
T
+
V
{\displaystyle {\mathcal {H}}=T+V}
).
In field theory,
V
{\displaystyle V}
always contains 3 fields terms or more, expressing for example that an initial electron (field 1) interacted with a photon (field 2) producing the final state of the electron (field 3). In contrast, the kinetic part
T
{\displaystyle T}
always contains only two fields, expressing the free propagation of an initial particle (field 1) into a later state (field 2).
The coupling constant determines the magnitude of the
T
{\displaystyle T}
part with respect to the
V
{\displaystyle V}
part (or between two sectors of the interaction part if several fields that couple differently are present). For example, the electric charge of a particle is a coupling constant that characterizes an interaction with two charge-carrying fields and one photon field (hence the common Feynman diagram with two arrows and one wavy line). Since photons mediate the electromagnetic force, this coupling determines how strongly electrons feel such a force, and has its value fixed by experiment. By looking at the QED Lagrangian, one sees that indeed, the coupling sets the proportionality between the kinetic term
T
=
ψ
¯
(
i
ℏ
c
γ
σ
∂
σ
−
m
c
2
)
ψ
−
1
4
μ
0
F
μ
ν
F
μ
ν
{\displaystyle T={\bar {\psi }}(i\hbar c\gamma ^{\sigma }\partial _{\sigma }-mc^{2})\psi -{1 \over 4\mu _{0}}F_{\mu \nu }F^{\mu \nu }}
and the interaction term
A coupling plays an important role in dynamics. For example, one often sets up hierarchies of approximation based on the importance of various coupling constants. In the motion of a large lump of magnetized iron, the magnetic forces may be more important than the gravitational forces because of the relative magnitudes of the coupling constants. However, in classical mechanics, one usually makes these decisions directly by comparing forces. Another important example of the central role played by coupling constants is that they are the expansion parameters for first-principle calculations based on perturbation theory, which is the main method of calculation in many branches of physics.
Hey there!
I am still rather new to renormalising QFT, still using the cut-off scheme with counterterms, and have only looked at the φ^4 model to one loop order.
In that model, we renormalise with a counterterm to the one-loop four-point 1PI diagram at a certain energy scale.
Do I simply, in...
I am heavily confused about the coupling constants. I primarily refer to this source https://www.physicsmasterclasses.org/exercises/keyhole/en/projects/running_alphas.html , but other sources were not able to lift my confusion either.
First, in the figure, the scales appear as quite failed. The...
The set of quantum numbers for the 4p orbital is: 4, 1, {-1,1}, +-1/2 (n,l,m,s)
The set of quantum numbers for the 4d orbital: 4,2,{-2,2},+-1/2
Hence we can calculate DeltaE for the 4p sub levels for j=1+- 1/2
And for the 4d sub levels as j=2+-1/2.
Giving four total values for Delta E as:
C_4p...
Hi all, I am sure I am missing something really elementary, but I would really appreciate someone pointing it out to me. So, if we consider the situation in abelian gauge symmetry, say for fermion matter ψ, of charge q. The transformation law for ψ is,
ψ→ψ' = e[- i q θ(x)] ψ.
We then have to...
Links for context:
1. https://en.wikipedia.org/wiki/Yukawa_potential
2. https://en.wikipedia.org/wiki/Yukawa_interaction#Classical_potential
I'm working on my BSc right now and I'm solving the energies of 2 nucleon systems (so basically just deuteron) by treating them as non-relativistic two...
Homework Statement
Vertex Feynamnn rule for computing the time correlator of fields under an action such as, for example,
Say ##S_{int} [\phi] =\int d^4 x \lambda \frac{\phi^4(x)}{4!} + g \frac{\phi^4(x)}{4!} ##, ##\lambda## and ##g## the coupling constants.
Homework Equations
see below...
Most QFT texts, such as Peskin&Schroeder and D. Tong's lecture notes, contain a mention that the renormalizability of an interacting theory requires the coupling constants to have correct dimensions, making scalar fields with ##\phi^5 , \phi^6, \dots## interactions uninteresting. Maybe there are...
In analogy to the fine structure constant, the dimensionless coupling constant of gravity is defined as some reference mass divided by the Planck mass, squared.
But what is the reference mass?? I have read thread...
I'm having a hard time understanding the mechanism of J coupling in NMR. Why is coupling information only transmitted through bonding electrons with nonzero s-character? For example, why can't coupling information be transmitted through a bond with no s-character, e.g. a retrodative bond...
I know that QFT puts in the coupling constants by hand, based on experiment. And many of the coupling constants are suppose to become equal at the grand unification energy. But I wonder if there is any principle that would allow us to calculate the present day coupling constants based the GUT...
How would it make any sense to use dimensionless numbers to represent physical things?
From wikipedia:
If you are comparing the strength of forces, and you are using these numbers to do so, I would have thought that these numbers would represent units of - well, force.
Clearly I must...
I was thinking about units and started wondering about coupling constants. In unit-independent form, the fine-structure constant is defined as \alpha = \frac{k_e e^2}{\hbar c}
I don't have a deep knowledge of particle physics but I know that there are weak and strong charges which enter the...
I understand that by uncertainty relations, it is possible use an EFT to a range of energy, forgotten the interactions for bigger energies. But, ¿ why change the values of coupling costants?
And, ¿ how can tell that there is no intermediate particle that happens with low probability in...
How is the effective (or renormalized) coupling constant at a given momentum scale scale measured?
If one wants a definition which makes it easy to measure I would think it would be natural to use the LSZ formula which connects the measurable Feynman amplitude with the amputated greens...
I've been trying to compute the bending-torsion coupling constants for a wing, B1, B2 and B3. The expression for this is
\begin{bmatrix} B_1 \\ B_2 \\ B_3 \end{bmatrix} = \iint (y^2 + z^2)\begin{bmatrix} y^2 + z^2 \\ z \\ y \end{bmatrix}dydyz
where x is in along the wingspan direction, y...
background:
I have a HNMR spectra and I am trying to figure out what is coupled to what. There is a set of 4 doublets where it is know that there 2 sets of coupled doublets. the doublets have j-values of 8.8 @ 8.04ppm, 8.8@ 7.58ppm, 8.4@7.39ppm and 8.4@7.00ppm. While I may have assumed that...