math&physics with intuition
math&physics with intuition
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Heuristic Derivation of Path Integrals from Classical Field Theory (including Schwinger Principle)
A heuristic derivation of the path integral, starting from the Schwinger dynamical principle. This approach bridges classical field theory and quantum mechanics by considering small variations in the action.
The Schwinger principle is derived by relating changes in the action to quantum transitions.
This forms the foundation of the path integral formalism, where the sum over all possible field configurations determines the quantum evolution of a system.
#QuantumFieldTheory #SchwingerPrinciple #PathIntegral #ClassicalToQuantum #TheoreticalPhysics #FieldTheory #QuantumMechanics #ActionPrinciple #MathematicalPhysics #PhysicsResearch #mathematics #mathlover #physicslover
Переглядів: 0

Відео

Reynolds transport theorem: derivatives of time-dependent volume integrals
Переглядів 84День тому
The time derivative of a volume integral often appears in physics, particularly in the context of conservation laws and field theories. For example, in electromagnetism, the continuity equation relates the time derivative of the charge density to the divergence of the current density. The derivation shown in the video is an informal way of thinking about the transport theorem (which is related ...
Gauss Curvature and proof of Gauss Theorema Egregium
Переглядів 6314 днів тому
In this post, we explore the concept of Gaussian curvature on surfaces within three-dimensional space. These fundamental aspects of differential geometry lead us to the celebrated "Theorema Egregium," a theorem discovered by the renowned mathematician Carl Friedrich Gauss. #DifferentialGeometry #Curvature #PrincipalCurvatures #MathematicalTheory #Mathematics #STEMEducation #AdvancedMath #geomet...
Normal curvature and principal curvatures (surfaces in 3 dimensions)
Переглядів 4221 день тому
In this video, we delve into the concepts of normal curvature and principal curvatures on surfaces within three-dimensional spaces. These fundamental aspects of differential geometry allow us to understand how the normal curvature on the surface can be rigorously determined through the ratio between the second fundamental form and the first fundamental form. The discussion includes the relation...
Gradient in spherical coordinates (derivation using concepts of tensor calculus and linear algebra)
Переглядів 10128 днів тому
Presented here is a detailed algorithm for computing the components of the gradient in spherical coordinates. Although this is a simple exercise usually seen in basic multivariable calculus courses, the pictures illustrate some concepts which might be inferred from tensor calculus. For further insights, refer to the accompanying video where these relations are rigorously proven and implemented ...
Derivation of the strain tensor in spherical coordinates
Переглядів 69Місяць тому
Presented here is a detailed algorithm for computing the components of the strain tensor in spherical coordinates. The picture illustrates each step, starting with the definition of the displacement vector (in spherical coordinates) and transformation matrix (from cartesian to spherical), and culminating in the derivation of the strain tensor matrix. For further insights, refer to the accompany...
Fourier series expansion for thin plates
Переглядів 57Місяць тому
Application of Fourier series in two dimensions. For thin plates, there is a simple method for finding the displacement and stress when a plate is simply supported (displacements and bending moments are zero on the boundary). The idea is to use a double Fourier series. #FourierSeries #Mathematics #STEM #MathIsBeautiful #AdvancedMath #MathLover #fourier #mathematician #physics #physicslover #the...
Physics of thin plates derived from the variational principle (bending and twisting moments, etc)
Переглядів 40Місяць тому
Exploring the classical theory of thin plates, we delve into the relations between moments, shear forces, external forces, and derivatives of displacements. These fundamental equations describe the behavior of a thin plate under small deformations, with (possibly) external forces acting upon it. We derive the equations from an action principle. #ThinPlates #StructuralMechanics #EngineeringMathe...
Classical Theory of Thin Plates derived from the Action Principle
Переглядів 72Місяць тому
Exploring the classical theory of thin plates, we delve into the constitutive relations between stresses and strains, as well as their connection to displacement and deformation. These fundamental equations describe the behavior of a thin plate under small deformations, with no external forces acting upon it. Through a rigorous mathematical framework, we derive that the minimization of the ener...
Minimal surfaces in calculus of variations
Переглядів 72Місяць тому
In mathematics, a minimal surface is a surface that locally minimizes its area. Non-trivial solutions like the catenoid and the helicoid satisfy the minimal surface equation. #FourierSeries #Mathematics #MathIsBeautiful #ScienceAndMath#LearningMath #MathInspiration #MathematicalArt #AdvancedMath #MathLovers #mathematician #lovemath #physics #physicslover #theoreticalphysics #mathchallenge #math...
Markowitz Model for risk minimization in a financial portfolio
Переглядів 57Місяць тому
The goal of portfolio optimization is for an investor to achieve the best possible return while minimizing risk. In the Markowitz portfolio theory, risk is represented by the variance of the portfolio. Therefore, the problem is to minimize the portfolio variance while maintaining a given return. #finance # #FourierSeries #Mathematics #MathIsBeautiful #ScienceAndMath #MathGenius #LearningMath #M...
Derivation of the strain tensor in the theory of elasticity
Переглядів 94Місяць тому
This summary covers the key points and equations on the strain tensor. #FourierSeries #Mathematics #MathIsBeautiful #ScienceAndMath #MathGenius #LearningMath #MathInspiration #MathematicalArt #AdvancedMath #MathLovers #mathematician #lovemath #physics #physicslover #theoreticalphysics #mathchallenge #math #maths #theoryofelasticity
Black Scholes equation: mathematical derivation
Переглядів 94Місяць тому
The Black-Scholes partial differential equation is derived by constructing a riskless portfolio consisting of a stock and an option, applying Itô’s Lemma to find the differential of the option value, eliminating risk by choosing the appropriate hedge ratio, and then equating the riskless portfolio return to the risk-free rate. #finance # #FourierSeries #Mathematics #MathIsBeautiful #ScienceAndM...
Interesting Fourier series in 2 dimensions
Переглядів 562 місяці тому
Fourier series in two dimensions: We approximate a function using the Fourier series, demonstrating the elegance of mathematical solutions without relying on calculation of integrals. Check out how we break down the function of two variables: H(x,t)=t 2sin( 5πx/L) using a clever approach to find the coefficients. It really seems as if magic appears behind these calculations, but it is not magic...
Geodesics on surfaces of revolution
Переглядів 792 місяці тому
A surface of revolution can be described by rotating a curve z=f(r) around the z-axis. By solving the geodesic equation, we are able to find the (implicit) form of geodetic curves, and also discuss whether "meridians" and "parallels" are geodesics. #mathematics #geodesics #geometry #MathIsCool #mathlove #science #engineering #mathmagic #curvedspaces #mathematicsrocks #mathcommunity #advancedmat...
Maupertuis principle derived from the more general action principle
Переглядів 2322 місяці тому
Maupertuis principle derived from the more general action principle
Poisson brackets and analogies with Quantum Mechanics
Переглядів 1822 місяці тому
Poisson brackets and analogies with Quantum Mechanics
Calculation of Inverse Laplace Transform using residues
Переглядів 842 місяці тому
Calculation of Inverse Laplace Transform using residues
Lorentz transformations and the Invariant Element in Special Relativity (Mathematical Derivation)
Переглядів 1052 місяці тому
Lorentz transformations and the Invariant Element in Special Relativity (Mathematical Derivation)
Intro to the Laplace Transform from the Fourier Transform
Переглядів 773 місяці тому
Intro to the Laplace Transform from the Fourier Transform
differential equation with Dirac delta and boundary conditions
Переглядів 1613 місяці тому
differential equation with Dirac delta and boundary conditions
Problem on multiple convolutions, Fourier Transforms, Distributions (edited)
Переглядів 2223 місяці тому
Problem on multiple convolutions, Fourier Transforms, Distributions (edited)
Faddeev Popov Ghost and Path Integrals
Переглядів 1423 місяці тому
Faddeev Popov Ghost and Path Integrals
A Nice Operator Identity with Nested Commutators
Переглядів 553 місяці тому
A Nice Operator Identity with Nested Commutators
Representations of Bessel function of order zero
Переглядів 313 місяці тому
Representations of Bessel function of order zero
Synthesis of Non Gaussian Signals with a Prescribed Fatigue Damage Spectrum (Research on Vibrations)
Переглядів 454 місяці тому
Synthesis of Non Gaussian Signals with a Prescribed Fatigue Damage Spectrum (Research on Vibrations)
Engineering Graphical User Interface for analyzing random vibration signals
Переглядів 584 місяці тому
Engineering Graphical User Interface for analyzing random vibration signals
“Smart” Engineering (aided by mathematics): Finding the Perfect Pipe Diameter to Minimize Costs
Переглядів 424 місяці тому
“Smart” Engineering (aided by mathematics): Finding the Perfect Pipe Diameter to Minimize Costs
Passion for mathematics and physics: material and courses
Переглядів 804 місяці тому
Passion for mathematics and physics: material and courses
Model on the evolution of epidemics
Переглядів 644 місяці тому
Model on the evolution of epidemics

КОМЕНТАРІ

  • @DavidQ-p2m
    @DavidQ-p2m 17 годин тому

    I have sometimes wondered if you can write every law of physics (thermodynamics, fluid dynamics...) with differential forms.

  • @jalsiddharth
    @jalsiddharth 2 дні тому

    Hey! Thank you so much for making this video. What I attempted was, I used MoC to solve for tau's PDE, and (while I don't 100% understand it yet), but realized that tau must be a function of C, and then I had a(C) just like in the paper. But then he says a = phi(v), and I'm "in general" lost about what's happening here. Secondly, I got stuck when I tried to substitute x' = x - vt back into xi, and (where gamma = lorentz factor), got a * 1/gamma^2 * (x - vt) and I got confused about what to do with the extra gamma. Then saw your video and you absorbed it into a(v), and here too I'm clueless. Can you please help /explain this? This is the only part in the derivation I'm not 100% clear on (perhaps my total lack of theoretical exploration in real analysis is the problem here), I barely managed to learn the characteristics method from youtube. Thank you so much :)

  • @Neetnotes9886
    @Neetnotes9886 9 днів тому

    sir please recommended a book where i find this topic related examples

  • @robmorgan1214
    @robmorgan1214 11 днів тому

    Holy crap. I understood your thumbnail! My flavor preferences are chocolate, vanilla, peppermint, asparagus, charm and pistachio. Up has a strange aftertaste but strange just tastes like marshmallows.

  • @SamCheryl-s6q
    @SamCheryl-s6q 11 днів тому

    Martinez Sharon Gonzalez Ruth Moore Linda

  • @ladbla1752
    @ladbla1752 13 днів тому

    Thanks for the video. Can you please let us know a practical example how to use Reynolds transport theorem ?

    • @yansongguo8354
      @yansongguo8354 13 днів тому

      In hydrodynamics you have a Eulerian picture and lagragian picture and the transport theorem is exactly the transformation between the operators between 2 pictures

    • @yansongguo8354
      @yansongguo8354 13 днів тому

      More specifically if think f as density rho the theorem gives Lagrangian derivative of mass is in fact the conservation law of mass in eular picture which is the right hand side of the equation

  • @Raphael4722
    @Raphael4722 17 днів тому

    Elegant

  • @Miguel64038
    @Miguel64038 Місяць тому

    Thanks for this video!!!

  • @rootjay
    @rootjay Місяць тому

    Tricky equations 😅 but you did the job well

  • @GeoffryGifari
    @GeoffryGifari Місяць тому

    Wonder if the parameter nu in the constitutive relation can be linked to the conservation of mass

    • @math.physics
      @math.physics Місяць тому

      Yes, Poisson's ratio can indeed be linked to the concept of mass conservation. Mass conservation can be used to evaluate it. Mathematically, if a material is stretched along the x-axis, causing a strain 𝜖_𝑥, the resulting strains in the perpendicular y and z directions are given by: 𝜖_𝑦=𝜖_𝑧=−𝜈𝜖_𝑥 ν is Poisson's ratio, which is typically a positive number for most materials. Mass conservation implies that during the deformation of a material, the mass of the material remains constant. For a given volume element of the material, if we assume the material is incompressible, then its density remains constant, which implies that any increase in one dimension must be exactly compensated by a decrease in other dimensions to maintain the same volume. Consider a small cubic element of the material with an initial volume 𝑉0=𝐿𝑥 𝐿𝑦 𝐿𝑧, where 𝐿𝑥, 𝐿𝑦, and 𝐿𝑧 are the initial lengths along the 𝑥, 𝑦, and 𝑧,axes, respectively. After deformation, the new dimensions become 𝐿𝑥′=𝐿𝑥(1+𝜖_𝑥), 𝐿𝑦′=𝐿𝑦(1+𝜖_𝑦), and 𝐿𝑧′=𝐿𝑧(1+𝜖_𝑧) The new volume 𝑉′ after deformation is: 𝑉′=𝐿𝑥′𝐿𝑦′𝐿𝑧′=𝐿𝑥(1+𝜖_𝑥)⋅𝐿𝑦(1+𝜖_𝑦)⋅𝐿𝑧(1+𝜖_𝑧) For small strains, the volume can be approximated as: 𝑉′≈𝑉0(1+𝜖_𝑥+𝜖_𝑦+𝜖_𝑧) For mass conservation in the case of an incompressible material, the volume must remain constant, so 𝑉′=𝑉0 This implies: 𝜖_𝑥+𝜖_𝑦+𝜖_𝑧=0 Substituting the relationship between longitudinal and transverse strains (using Poisson's ratio): 𝜖_𝑥−𝜈𝜖_𝑥−𝜈𝜖_𝑥=0 This implies that for incompressible materials, Poisson's ratio 𝜈=1/2

    • @GeoffryGifari
      @GeoffryGifari Місяць тому

      @@math.physics thank you for the comprehensive explanation

  • @GeoffryGifari
    @GeoffryGifari Місяць тому

    Ah so the equation including W is for bending?

    • @math.physics
      @math.physics Місяць тому

      w(x,y) is the displacement of the generic point (x,y) of the plate in the direction z perpendicular to the plate. In the classical theory of thin plates, the derivatives of w are related to stresses, strains, bending moments, twisting moments, shear forces, etc.

  • @rootjay
    @rootjay Місяць тому

    🎉🎉 👏👏 🥇🏅

  • @rootjay
    @rootjay Місяць тому

    This equation needs alot of data 😅

  • @marcoantoniazzi1890
    @marcoantoniazzi1890 Місяць тому

    Could you please explain to me why physicists before Einstein could not have arrived at the final formula?

  • @rootjay
    @rootjay Місяць тому

    Is it used for prediction model ?

    • @math.physics
      @math.physics Місяць тому

      There are several applications that demonstrate the versatility of the Black-Scholes model in the financial world, particularly in derivatives trading and risk management (I don't have much experience with that though)

  • @plranisch9509
    @plranisch9509 Місяць тому

    nagyon jó

    • @math.physics
      @math.physics Місяць тому

      @@plranisch9509 köszi, azt hiszem, egy év alatt szépen fejlődtem (mármint ehhez a videóhoz képest) :)

  • @calvinjackson8110
    @calvinjackson8110 Місяць тому

    Not following you. Where is the paper I see in the cover photo so I can just read it?

  • @cristianofernando-l3i
    @cristianofernando-l3i Місяць тому

    can u pls do a full review of the exam paper im in supirioe terza

  • @rootjay
    @rootjay 2 місяці тому

    Interesting problem

  • @rootjay
    @rootjay 2 місяці тому

    Bit tricky for me to understand but good explanation 🎉

  • @rootjay
    @rootjay 2 місяці тому

    How can we find length of a curve

  • @goyohan1724
    @goyohan1724 2 місяці тому

    Exuse me, I have one question. This is not really related to the topic of the video. Do you know how to plot magnetic field lines in the Schwarzschild metric in wolfram mathematica? Or do you know where i can read about this? You're my last hope :( i want to learn. Thank you in advance

  • @rootjay
    @rootjay 2 місяці тому

    🎉🎉 🏅🏅

  • @rootjay
    @rootjay 2 місяці тому

    Interesting problem

  • @advantagerealty
    @advantagerealty 2 місяці тому

    Thank you i'm watching all your videos.

  • @advantagerealty
    @advantagerealty 2 місяці тому

    The nitty grity is the most beautiful, yet doesn't appear so.

  • @rootjay
    @rootjay 2 місяці тому

    🎉🎉 🏅🏅

  • @marcosgutierrez7593
    @marcosgutierrez7593 2 місяці тому

    You are a genius, I mean it seriously, and thank you so much for your work. Really amazing and so cool to explain the Einstein theories!!!

  • @foeldesi
    @foeldesi 3 місяці тому

    very useful video, there's a lot of false information out there about this, falsely stating that kinetic energy in QM can be negative.

  • @giammarcomanetti5656
    @giammarcomanetti5656 3 місяці тому

    Ciao, fai anche ripetizioni? dove posso contattarti? Grazie

  • @rootjay
    @rootjay 3 місяці тому

    🎉🎉 🥇🥇🏆🏅 good content

  • @curtischee2532
    @curtischee2532 3 місяці тому

    Great proof. Please do more videos.

  • @森聡一郎
    @森聡一郎 3 місяці тому

    Really nice! The explanation is so clear and easy to understand.

  • @andrewbodor4891
    @andrewbodor4891 3 місяці тому

    I submit that what causes the two plates to come closer is Quantum space; specifically the gravity created by that space. Matter and quantum space repel each other. Around the earth the quantum space density is great and lessons by distance from the earth. The plates are pressed together by this dense quantum space. To prove my theory take the Casimir experiment to the ISS and do it where the quantum space, the pressure of it, gravity, is less. If I am correct the plates should not come together as readily since the pressure of the quantum space, gravity, is much less. Prove me wrong

  • @rootjay
    @rootjay 3 місяці тому

    Interesting problem 🎉🎉

  • @hosz5499
    @hosz5499 3 місяці тому

    how do you generalise to evaluate zeta(4) with integrate_0^1 1/(1-xyzw) dx dy dz dw --> Pi^4/90?

  • @rootjay
    @rootjay 3 місяці тому

    Interesting problem

  • @ahadamin7361
    @ahadamin7361 3 місяці тому

    I love your accent ❤❤❤

  • @tunaphobe
    @tunaphobe 3 місяці тому

    I like this proof. A smart little trick at the beginning and just raw dogging till the end. Euler would be proud.

  • @rootjay
    @rootjay 3 місяці тому

    🎉🎉🏅🏅

  • @mortimertz6660
    @mortimertz6660 3 місяці тому

    very well explained. thank you!

  • @mortimertz6660
    @mortimertz6660 3 місяці тому

    thanks

  • @mortimertz6660
    @mortimertz6660 3 місяці тому

    nice

  • @mortimertz6660
    @mortimertz6660 3 місяці тому

    very good

  • @mortimertz6660
    @mortimertz6660 3 місяці тому

    very good

  • @mortimertz6660
    @mortimertz6660 3 місяці тому

    very good demonstration. thank you.

  • @rootjay
    @rootjay 3 місяці тому

    🎉🎉 🥇🥇

  • @stevenlin6106
    @stevenlin6106 4 місяці тому

    This is great. Could you share who invented this argument in history?

  • @rootjay
    @rootjay 4 місяці тому

    🎉🎉🏅🏅