A convention is a set of agreed, stipulated, or generally accepted norms. It typically helps common efficiency or understanding but is not required, as opposed to a strict standard or protocol.

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Complex scalar field theory

For the complex scalar field theory $$L = -\partial_{\mu}\phi^{*}\partial_{\mu}\phi - m^{2}\phi^{*}\phi + J\phi^{*}+J^{*}\phi,$$ Why is there no factor of 1/2 in the lagrangian like in the real ...
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225 views

Performing Wick Rotation to get Euclidean action of scalar field

I'm working with the signature $(+,-,-,-)$ and with a Minkowski space-stime Lagrangian $$ \mathcal{L}_M = \Psi^\dagger\left(i\partial_0 + \frac{\nabla^2}{2m}\right)\Psi $$ The Minkowski action is $$ ...
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53 views

How can you tell if the work done by a force is negative?

This is kind of confusing to me. I'm guessing that it's specific to the problem. Is the work done by friction always negative? Is the work done by gravity always negative? Spring as well? It seems ...
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64 views

Sign of induced EMF and other elements in AC circuit

I am having problems to determine the direction of the induced EMF in AC circuits. For example, we have an inductor of inductance $L$. The induced EMF is given by: $$ \epsilon = - L \frac{di}{dt} $$ ...
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87 views

Limits of Integration Trig, Mag Field Infinite Length Wire

I don't understand how the limits of integration should be defined when doing basic integrals of trig functions. It seems like it's an arbitrary decision, I don't understand it. Here's the set up: ...
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Can we define tension in a string as the reactive force produced in a string being pulled at both ends?

In my textbook, the definition of tension was given that Tension is the reactive force which exists when string is being stretched at its both end. After it there was a case given that to calculate ...
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31 views

Sig Figs, Combined Operations

Using the sig fig rule for addition / subtraction seems to break in certain circumstances. For example (I'm using underlines to show sig figs): $\underline{66}+\underline{66}-\underline{1.3}\times ...
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105 views

Proportionality Constant in Einstein Field Equations

The Einstein Field Equations: $$G_{ab}~=~8\pi T_{ab}.$$ I am familiar with how to obtain the $8\pi$ proportionality factor through correspondence with Newtonian gravity, but am wondering if this ...
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414 views

Fourier Transforms of position and momentum space in Quantum Mechanics

Fourier transformations: $$\phi(\vec{k}) = \left( \frac{1}{\sqrt{2 \pi}} \right)^3 \int_{r\text{ space}} \psi(\vec{r}) e^{-i \mathbf{k} \cdot \mathbf{r}} d^3r$$ for momentum space and $$\psi(\vec{r}...
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68 views

Wave equation in classical mechanics!

We represent the wavefunction of any wave on the string as $$y=f(x-vt),$$ where $v$ is velocity of the wave and $x$ is distance from origin and $t$ is time taken to reach the given point and $y$ is ...
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78 views

Different definitions of the parity transformation for the Dirac spinors

There are two definitions of the parity transformation acting on the Dirac spinors: $\Psi_P = \eta \gamma^0 \Psi$ with $\eta = i$ ($P^2=-1$ as in Srednicki) and $\eta=1$ ($P^2=+1$ as in Peskin & ...
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62 views

Conventions and realities of kinetic energy?

I am having doubts regarding why $1/2$ is present in kinetic energy and if this is conventional why cant we say potential energy is $2mgh$ and kinetic energy $mv^2$. So is this $1/2$ conventional or ...
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45 views

Is the net force conventionally shown in a free body diagram?

Is it standard convention to display the net force vector on a free body diagram? Internet searches seem to give mixed results.
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1answer
201 views

How do you derive Fleming's left hand rule?

How do you derive Fleming's left hand rule? What is the theoretical explanation for the directions of the magnetic field, current and the force on the current for being oriented in that way relative ...
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1answer
45 views

Why Does there Have to be Linearity in Ket and Skew Symmetry?

I'm reading Shankar's "Principles of Quantum Mechanics," and on page 8 he states that one axiom in Dirac notation is linearity in ket, and because they are also skew symmetric there is anti-linearity ...
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1answer
46 views

EFE and Local Minkowski

Suppose we view the Einstein Field Equations (EFE) in the context of a boundary value problem with a given stress-energy tensor and boundary conditions. The problem is solved by finding a pseudo-...
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1answer
31 views

How to determine the direction of arrow on Feynman diagram for $W$ boson line?

I am somewhat confused. Looking through these slides (especially the 11th), which show Feynman diagrams involving $W$-bosons, I can't figure out which way to draw the arrow near the $W$ boson? How do ...
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19 views

About Electric potential

when we bring a unit positive charge from infinity to a point in the electric field EF does work on the charge and external work is also done on the charge in same amount but in opposite sign. then ...
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96 views

Rocket equation derivation mistake by my professor

In one of my lectures our physics professor gave a derivation of the ideal rocket equation as follows: Let $v_G > 0$ be the velocity at which the gas is emitted from the rocket. Let $m$ and $v$ be ...
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26 views

Negative ampere and graphical convention

Since only electron's flow in electricity and electrons have negative charge, then why we don't say —1amps (—1C/s)? Secondly, as conventional way we write down independent variable in $x$ axis and ...
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1answer
190 views

How can energy be negative in a finite square well?

Say if the potential $V(x) < 0$ in the well but the sides or the scattered states its zero potential, anyways How is that the energy in the well is less than zero? Is it because the potential ...
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1answer
132 views

Confused regarding sign convention of silvered plano convex lens

I'm totally confused while finding the sign convention of a silvered plano convex lens. I know that equivalent power of such a system can be found by adding the power of the mirror and twice the power ...
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40 views

Integration path with opposite direction from the unit vector

The task is to calculate the voltage between points $M$ and $N$ if the electric field vector is known to be $\vec{E}=\frac{V_0\cdot x^2}{a^3} \cdot \vec{i} + \frac{V_0 \cdot y}{a^2} \cdot \vec{j}$, ...
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102 views

What does “Receptor” convention refers to in RC circuits?

my question is How can we choose the convention in a circuit and what does it refer to ? Especially for a Capacitor I hear the terms "passive sign convention..." "receptor convention ..." "generator ...
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43 views

Why is it said that electric current always flow from higher potential to lower potential?

Why is it said that electric current always flow from higher potential to lower potential? It is said that current flows from positive terminal to negative terminal, but it is actually the negative ...
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Why are generators defined oppositely in Weinberg's vs. Maggiore's QFT books?

I've been confused about the sign conventions used in Weinberg's QFT book for a long time. Here's my question: The generators $J^{\mu\nu}$ are defined in this book as $$U(1+\omega)=1+\frac{i}{2}\...
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Correct way to define parity of two parafermions

I am checking the literature on parafermions and it seems that people define the parity of two parafermions to be $\gamma_{a}^{-1}\gamma_{b}$. Is this definition always valid? How does one come up ...
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103 views

What decides the signs and coefficients of terms in superfield?

I'm working on a problem in 3d field theory and I'm confused about how to write the superfields. Specifically, I'm not sure if the signs and coefficients of terms are purely a matter of convention or ...
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441 views

Dirac action and conventions

I have a (possibly) fundamental question, which is driving me crazy. Notation When considering the Dirac action (say reading Peskin's book), one have $\int dV\;\bar{\psi}\left(\imath\not\partial-m\...
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Conventions in defining spherical harmonics and associated Legendre polynomials

Relevant Background Spherical harmonics are defined with several different conventions: the definition used in quantum mechanics according to Wikipedia is $Y_l^{\,m}(\theta,\phi) = (-1)^m\sqrt{\frac{...
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Where do the intrinsic parities of particles come from?

It is known that some particles have negative intrinsic parity - for example pion $\pi$. I was wondering if this parity can be understood. I read somewhere that parity of quarks is defined to be ...
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General proof of formulas of geometric optics?

In most lf textbooks formulas of geometric optics like lens maker formula and base formula for that are proven (or rather verified from my point of view) by taking specific case (ray diagram) and ...
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What is “above” and what is “below” the surface of a sphere?

When studying Electromagnetism using D.J. Griffith's Introduction to Electrodynamics, the boundary conditions for the electric potential across a surface charge density are expressed using the normal ...
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99 views

Question about Origins in Galilean transformation

I'm just learning about relativity, and every equation I see for a galilean transformation of frame $S'$ (moving with uniform velocity in the $x$-direction with respect to frame $S$) is $x'=x-vt$, $y'=...
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Convention in physics for [],{} and operators (QM)

I got a little mixed up with the convention in physics. Usually a hat means an operator. For a given electron-ion Hamiltonian $\hat{H}_{e-n}$, what are the difference between these: 1) $\hat{H}_{e-...
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Sign convention with the $AdS$ metric

One would say that $AdS_n$ satisfies the equations for the scalar curvature (R) and Ricci tensor ($R_{\mu \nu}$), $R = - \frac{n(n-1)}{L^2}$ and $R_{ab} = - \frac{n-1}{L^2}g_{ab}$. But do the signs ...
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Minus sign in analyzing RC with changing emf circuit?

I'm learning electromagnetism from Purcell's book. He say that if we have the following circuit: $$-\frac QC + RI = \mathcal E_0\cos\omega t~,\quad I = -\frac{\mathrm dQ}{\mathrm dt} $$ The ...
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Doubts about Chern-Simons state as a solution of the Hamiltonian constraint in quantum gravity

I've been doing some work with both Baez's Knots, gauge fields and gravity (1) and Gambini, Pullin's Loops, knots, gauge Theories and quantum gravity (2), lately. I have basically two problems: I ...
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Why is surface tension positive?

My book describes surface tension as $e=dW/dA$ and work as being negative when it is done against a force. Therefore, if i increase the surface area of a liquid i am doing work on the liquid against ...
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What is the direction of area vector while calculating flux in AC generators?

I was told that in case of an open surface, the direction of area vector is considered to be in the direction of magnetic field but my doubt is won't the direction of area vector change as armature ...
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32 views

The sign of a focal length

We know that for converging lens, $f>0$ , for diverging lens, $f<0$. But for many materials I have read so far, it says that: "the focal length of a concave lens is 8 cm." I thought that the ...
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63 views

About the definition of super Hilbert Spaces

I have founded in the literature at leas two different definition of Hilbert spaces: Definition 1: A super Hilbert space is a complex super-vector space $\mathcal{H}=\mathcal{H}_0\oplus \mathcal{H}...
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FRW Metric maximally symmetric, derivation, $R=3K$ or $R=6K$ confusion, two different texts

I'm looking at Tod and Hughston Introduction to GR and writing the metric in the two forms; [1]$$ ds^{2}=dt^{2}-R^{2}(t)(\frac{dr^{2}}{1-kr^{2}}+r^{2}(d\theta^{2}+sin^{2}\theta d\phi^{2})) $$ [2] $$ ...
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91 views

Sign error in calculating the electric field of point charge

I have to determine the electric field of a point charge, I get a true result except for a sign. Here is my passages. $$\nabla \cdot e = \frac{\rho}{\epsilon}$$ $$e = - \nabla u$$ $$\nabla^2 u = - ...
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Feynman graph, proportional charge of a vertex

It is defined that the contribution of a vertex in a Feynman Graph towards the probability amplitude $ M_{fi} $ is proportional to a charge $Q_f$. Yet I seem to cannot find any precise explanation how ...
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A question about Majorana equation in Zee's QFT book

In chaper 2.1 of Zee's book(1st edition), he says that the majorana eqation $$i \gamma^{\mu}\partial_{\mu}\psi=m\psi_{c}$$ can be obtained from the Lagrangian:$$L=\bar{\psi}i\gamma^{\mu}\partial_{\mu}\...
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Need some help understanding Relativistic Notation

My question originates from what is done in the book on Quantum Field Theory book by Mark Srednicki on page 21 (if anyone has it). So say you have an inertial frame that is represented in the ...
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Index Placement for Spinors in Relativity

This may ultimately be a silly question, but a pedantic mind like mine gets tied into knots over differing notation. (Disclaimer: I'm a mathematician.) Let $\mathbb{W}$ be a complex two-dimensional ...
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Sign convention thermodynamics

Say a system is inside a volume $V$ with surface normal vector $n$ pointing out from the volume. Then there are force vector fields (nonconservative and conservative) depending on parameters external ...
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When heat is rejected by a system what will be $q$ according to sign convention?

When a system rejects heat it can be assumed that work is done by the system. So as per law the sign convention must be negative. But my physics textbook says the reverse. So is the question.